Home page of Stepan OREVKOV

Home pages of some of my co-authors:
Shustin Viro

Divers:
Monument to Pierre Fermat in Toulouse: jpg
zagadka

Programs (C, Mathematica, TeX/PS):

MayaPS: Typing Maya with TeX/LaTeX. Enter
Reference Manual (36 pages): ps.gz (228 K) pdf (900 K)

Vectorizer producing very short EPS. cotrace.zip (12K) README

Simplex method. o-simplex.zip (6K) README

Program for Fiedler's [ref]invariant. program README(pdf)

Quasipositivity problem for 3-braids qp3.m

On commutator subgroups of Artin groups
by S.Yu.Orevkov
Doklady Math. (to appear)
in Russian: ps.gz (59 K) ps (163 K) pdf (151 K) in English: ps.gz (109 K) ps (227 K) pdf (86 K)

Some examples of real algebraic and real pseudoholomorphic curves
by S.Yu.Orevkov
In: Proc. of Conf. "Perspectives in Analysis, Geometry and Topology" on the occasion of Oleg Viro's 60-th birthday. Progress in Math., Birkhauser (to appear)
ps.gz (543 K) ps (1356 K) pdf (655 K)

Agnihotri-Woodward-Belkale polytope and the intersection of Klyachko cones
by S.Yu.Orevkov and Yu.P.Orevkov
Mat. Zametki, 87(2010), no. 1, 101-107 (in Russian) pdf (240 K) ps.gz (90 K)
English transl.:Math. Notes, 87(2010), no. 1-2, 96-101 dvi (32 K) pdf (187 K) ps.gz (158 K) abstract

Proper analytic embedding of CP¹ minus Cantor set into C².
by S.Yu.Orevkov
Uspekhi Mat. Nauk, 63(2008), no. 1(379), 155-156 (in Russian)
English transl.: Russian Math. Surveys,, 63(2008), 168-169
Abstract: We construct what is in the title. ps pdf

Example of a continuous mapping S² --> R² whose set of fold points is dense in S².
by S.Yu.Orevkov
Abstract: We construct a mapping f : S² --> R² such that { p | f^-1 (f(p))={p}} is dense in S² .
pdf (129K) ps (328K) ps.gz (135K)

A la recherche de la topologie projective. Du cote de chez Arnold.
by S.Yu.Orevkov
Talk on the International Conference "Arnold-70", Moscow, August 20-25, 2007 ps (157 K) pdf (55 K)

Arrangements of an M-quintic with respect to a conic which maximally intersects its odd branch
by S.Yu. Orevkov
Algebra i Analiz, 19(2007), no.4, 174-242 (in Russian) pdf (964 K) ps (1.8 M) ps.gz (510 K)
English transl.: St. Petersbourg Math. J., 19(2008), 625-674 pdf (903 K) ps.gz (580 K) abstract

Sharpness of Risler's upper bound for the total curvature of an affine algebraic hypersurface
by S.Yu. Orevkov
Uspekhi Mat. Nauk, 62(2007), no. 2(374), 169-170
English transl.: Russian Math. Surveys, 62(2007), 393-394 tex (amstex, 5 K) pdf (75 K) ps (195 K) ps.zip (93 K) abstract

Algebraic curve in the unit ball in C² passing through the origin, all of whose boundary components are arbitrarily short
To the memory of Anatoliy Georgievich Vitushkin
by S.Yu. Orevkov
Trudy Mat.Inst. im. V.A.Steklova. 253(2006), 135-157. pdf (497 K) ps (833 K) ps.zip (274 K)
English translation: Proc. Steklov Inst. of Math. 253(2006), 123-143. pdf (435 K) ps (858 K) ps.zip (344 K) abstract

Plane real algerbaic curves of odd degree with a deep nest
by S.Yu. Orevkov
J. of Knot Theory and Ramifications, 14(2005), 497-522.
pdf (354 K) ps (754 K) ps.zip (303 K) abstract

Quasipositivity problem for 3-braids
by S.Yu. Orevkov
Proceedings of 10th Gokova Geometry-Topology Conference 2004, pp. 89-93.
Reprinted in: Turkish Journal of Math., 28(2004), 89-93.
pdf (154 K) ps (272 K) ps.gz (127 K) dvi (29 K) abstract

The number of trees half of whose vertices are leaves and asymptotic enumeration of plane real algebraic curves
by V.M. Kharlamov and S.Yu. Orevkov
J. of Combinatorial Theory, Ser. A, 105(2004), 127-142
pdf(225 K) ps(307 K) ps.gz (100 K) dvi (57 K) abstract

Solution of the word problem in the singular braid group
by S.Yu. Orevkov
Proceedings of 10th Gokova Geometry-Topology Conference 2004, pp. 95-100.
Reprinted in: Turkish Journal of Math., 28(2004), 95-100.
pdf (160 K) ps (135 K) ps.gz (55 K) dvi (25 K) abstract

Pseudoholomorphic algebraically unrealizable curves
by S.Yu. Orevkov and E.I. Shustin
Moscow Math. J., 3(2003), no.3, 1053-1083
pdf (709 K) ps (1126 K) ps.gz (434 K) abstract

Construction of arrangements of an M-quartic and an M-cubic with a maximal intersection of an oval and the odd branch
by S.Yu.Orevkov
Bulletin (vestnik) of Nizhni Novgorod State University,Ser. Math. Modeling and Optimal Control, issue 1(25),2002, 12-48
ps (Russian) (4754 K = 4.7 M) ps.gz (Russian) (1307 K = 1.3 M) pdf (Russian) (2141 K = 2.1 M)
English translation (is not supposed to be published):
ps (English) (4621 K = 4.6 M) ps.gz (English) (1287 K = 1.3 M) pdf (English) (2104 K = 2.1 M) abstract

Markov theorem for transversal links
by S.Yu. Orevkov and V.V. Shevchishin
J. of Knot Theory and Ramifications, 12(2003), 905-913
pdf (230 K) ps (257 K) Extended version: pdf (289 K) ps (335 K) abstract

New M-curve of degree 8
by S.Yu. Orevkov
Funct. Analysis and Appl., 36(2002), 247-249
Abstract: We construct a real algebraic curve of degree 8 with the real scheme 7 U 1<2 U 1<11>>
pdf (English) (125 K) pdf (Russian) (177 K) ps (English) (189 K) ps (Russian) (200 K)

Classification of flexible M-curves of degree 8 up to isotopy
by S.Yu. Orevkov
GAFA - Geometric and Functional Analysis, Vol. 12(2002), no.4, 723-755
In an appendix of this paper we give some computer programs used in the paper (see Abstract for more details).
pdf (522 K) ps (577 K) abstract

Counter-examples to the "Jacobian Conjecture at Infinity"
Dedicated to the seventieth birthday of Anatolii Georgievich Vitushkin
by S.Yu. Orevkov
Trudy Mat. Inst. im. V.A.Steklova, 235(2001), 181-210 (in Russian) pdf (484 K) ps (853 K)
English translation: "Proc. Steklov Math. Inst.", 235(2001), 173-201 pdf (431 K) ps (693 K)
abstract

Congruence modulo 8 for real algebraic curves of dergee 9
by   S.Yu. Orevkov    and   O.Ya. Viro
Uspekhi Mat. Nauk 56(2001), no.4, 137-138 (in Russian)
English translation: Russian Math. Surveys 56(2001), 770-771
abstract
pdf (77 K)     tex (amstex, 10 K)     dvi (13 K)     (the 2-page note published in "Russian Math. Surveys")
pdf (139 K)    tex (amstex, 13 K)     ps (124 K)     (a 3-page version of this text with more detailed computations)

Real quintic surface with 23 components
by S.Yu. Orevkov
C. R. Acad. Sci. Paris, Ser. I, 333(2001), 115-118
Abstract: We construct a real surface of degree 5 in $RP^3$ which has 23 connected components
pdf (184 K) ps (217 K) ps.gz (86 K)

Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves
by S.Yu. Orevkov
J. of Knot Theory and Ramifications, 10(2001), 1005-1023
pdf (361 K) ps (486 K) ps.gz (189 K) abstract

Quasipositivité d'une courbe analytique dans une boule pseudo-convexe (French; abridged English version)
[ Quasipositivity of an analytic curve in a pseudoconvex 4-ball]
by Michel Boileau and Stepan Orevkov
C. R. Acad. Sci. Paris, Ser. I, 332(2001), 825-830
pdf (140 K) dvi (32 K) tex (amstex, 26 K) abstract.tex (1 K) abstract

Petrovski-Oleinik inequalities and combinatorics of Viro T-hypersurfaces
by S.Yu. Orevkov
Algebra i Analiz, 14(2002), no.1, 134-157 (in Russian)
English translation: St.-Petersburg Math. J., 14(2003), no.1, 101-118
Appendix: Relative MacMullen inequalities (by R. MacPherson and S.Orevkov)
pdf (English) (281 K) pdf (Russian) (424 K) ps (English) (329 K) ps (Russian) (424 K)

Flexible, algebraically unrealizable curves: rehabilitation of Hilbert-Rohn-Gudkov approach
by S.Yu. Orevkov and E.I. Shustin
J. fur die Reine und Angew. Math., 551(2002), 145-172
pdf (505 K) ps (777 K) ps.gz (285 K) abstract

Asymptotic growth of the number of classes of real plane algebraic curves when the degree increases
by S.Yu. Orevkov and V.M. Kharlamov
Zapiski Nauch. Seminarov POMI, Vol. 266(2000), pages 218-233 (in Russian)
English translation: J. of Math. Sciences, 113(2003), no. 5, 666-674
pdf (206 K) tex (amstex, 41 K) dvi (53 K) ps (199 K)

A flexible affine M-sextic which is algebraically unrealizable
by S. Fiedler-LeTouzé‚ and S.Yu. Orevkov
J. of Algebraic Geometry, 11(2002), 293-310
pdf (385 K) ps (543 K) abstract

Markov moves for quasipositive braids
by S.Yu. Orevkov
C. R. Acad. Sci. Paris, Ser. I, 331(2000), 557-562
pdf (124 K) ps (208 K) abstract [Version abregé francaise: pdf (95 K) tex (amstex, 6 K) dvi (7 K)]

Strong positivity in the right-invariant order on a braid group and quasipositivity
by S.Yu. Orevkov
Mat. Zametki, 68(2000), no. 5, 692-698 (in Russian)
English translation: Math. Notes, 68(2000), 588-593
pdf (Russian) (225 K) ps (Russian) (290 K) abstract

Complex orientations of M-curves of degree 7
by S.Yu. Orevkov
In: Topology, Ergodic Theory, Real Algebraic Geometry. Rokhlin's Memorial. Amer. Math.Soc. Transl. ser 2. Vol. 202, 2001, pp. 215-227.
pdf (306 K) ps (501 K) ps.gz (184 K) abstract

Link theory and new restrictions for M-curves of degree nine
by S.Yu. Orevkov
Funct. Analysis and Appl., 34(2000), 229-231
tex (amstex, 13 K) dvi (17 K) ps (116 K) ps (Russian) (128 K) abstract

Projective M-cubics and M-quartics in general position with a maximally intersecting pair of ovals
by S.Yu. Orevkov and G.M. Polotovskii
St. Petersburg Math. J., 11(2000), 837-852
Abstract: A classification up to isotopy of curves mensioned in the title is obtained. The link theory (Murasugi-Tristram inequality) is used for restrictions.
pdf (Russian) (599 K) pdf (English) (562 K) ps (Russian) (599 K) ps (English) (562 K)

Projective conics and M-quintics in general position with a maximally intersecting pair of ovals
by S.Yu. Orevkov
Math. Notes, 65(1999), 528-532
Abstract: A classification up to isotopy of curves mensioned in the title is obtained. The link theory (Murasugi-Tristram inequality) is used for restrictions.
pdf (Russian) (203 K) pdf (English) (185 K) ps (Russian) (249 K) ps (English) (232 K)
WARNING FOR THOSE WHO WANT TO SUBMIT A PAPER TO "Math. Notes":
The technical editors of the journal "Matematicheskie Zametki" (translated in English as "Mathematical Notes") change the texts of the papers published in this journal. Moreover, they do not send galley proofs of English translations to the authors. To see a result of this practice, you may compare the original title of my paper (see above) with the title modified by the technical editors:
"Projective cones and M-quintics generic with respect to a maximally intersecting pair of ovals".
The incorrect title appeared in the published version. It was reproduced in MathSciNet and Zentralblatt.

The volume of the Newton polytope of a discriminant
by S.Yu. Orevkov
Uspekhi Mat. Nauk, 54(1999), no.5, 165-166 (in Russian)
English translation: Russian Math. Surveys, 54(1999), 1133-1134
pdf (82 K) tex (amstex, 10 K) dvi (15 K) ps (216 K) abstract

Riemann existence theorem and construction of real algebraic curves
by S.Yu. Orevkov
Annales de la Faculté des Sciences de Toulouse. Mathématiques, (6) 12 (2003), no. 4, p.517-531
pdf (440 K) ps (809 K) ps.gz (250 K) abstract
The list of the constructed new M-curves of degree 9 was incomplete in the version of this paper which was published as a preprint of Laboratoire Emile Picard (the version which was available on this site before 02/27/2003)

Asymptotic number of triangulations with vertices in Z²
by S.Yu. Orevkov
J. of Combinatorial Theory, Series A, 86(1999), 200-203
pdf (123 K) ps (80 K) abstract dvi file(14 K)

Potential at infinity of a polynomial image of the disk
by S.Yu. Orevkov
Funct. Analysis and Appl., 33(1999), 307-309
pdf (72 K) tex (amstex, 13 K) dvi (17 K) ps (196 K) pdf (Russian) (135 K) ps (Russian) (128 K) abstract

Singularity which has no M-smoothing
by V.M. Kharlamov, S.Yu. Orevkov, and E.I. Shustin
In: The Arnoldfest (Toronto, ON, 1997), Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999 pp. 273-309
Abstract: We give an example of a singulatity (of multiplisity 6 with 3 branches) for whose smoothings the local Harnack inequality is not sharp.
pdf (536 K) ps (811 K) ps.gz (288 K)

Link theory and oval arrangements of real algebraic curves
by S.Yu. Orevkov
Topology, 38(1999), 779-810; Erratum Topology, 41(2002), 211-212
Here we corrected numerous misprints appeared in the published version.
The modifications corresponding to the published erratum are also included here.
pdf (452 K) ps (696 K) ps.gz (227 K)

On rational cuspidal curves I. Sharp estimate for the degree via multiplicities
by S.Yu. Orevkov
Math. Annalen, 324(2002), 657-673
pdf (224 K) ps (514 K) abstract

On four-sheeted polynomial mappings of C² . I. The case of an irreducible ramification curve
by A.V.Domrina and S.Yu. Orevkov
Math. Notes, 64(1998), 732-744
pdf (231 K) ps (286 K) abstract

Acyclic algebraic surfaces bounded by Seifert spheres
by S.Yu. Orevkov
Osaka J. Math., 34(1997), 457-480
Here you find the version of the paper without numerous typos which are in the published version:
pdf (303 K) ps (302 K) abstract

Realizability of a braid monodromy by an algebraic function in a disk
by S.Yu.Orevkov
C. R. Acad. Sci. Paris, Ser. I, 326(1998), 867-871
pdf (168 K) ps (372 K) abstract

On rigid rational cuspidal plane curves
by S.Yu. Orevkov and M.G. Zaidenberg
Uspekhi Mat. Nauk, 51(1996), no. 1, 149-150 (in Russian); English translation: Russian Math. Surveys, 51(1996), 179-180
Abstract: A plane curve is called cuspidal if it has one branch at each singularity. We prove that a projectively rigid rational cuspidal curve has at most 9 singular points.
pdf (Russian) (146 K) ps (Russian) (140 K) ps.gz (Russian) (54 K)
pdf (English) (112 K) ps (English) (113 K) ps.gz (English) (47 K)

Plane curves with a big fundamental group of the complement
by G. Detloff, S.Yu. Orevkov, and M.G. Zaidenberg
In: Voronezh Winter Mathematical Schools, AMS Transl. Ser. 2, 184, AMS, Providence, RI, 1998, pp. 63-84
alg-geom/9607006

Rudolph diagrams and analytic realization of Vitushkin's covering
by S.Yu. Orevkov
Mat. Zametki, 60(1996), no. 2, 206-224 (in Russian)
English translation: Math. Notes, 60(1996), 153-164
pdf (English) (208 K) pdf (Russian) (279 K) abstract ps (English) (293 K) ps (Russian) (305 K) abstract

On Abhyankar quasirational singularities
by S.Yu. Orevkov
Uspekhi Mat. Nauk, 50:6(1995), 201-202(in Russian) pdf abstract
English transl.: Russian Math. Surveys, 50(1995), 1290-1291

On the number of singular points of plane curves
by S.Yu. Orevkov and M.G. Zaidenberg
In: Algebraic Geometry. Proc. Conf., Saintama Univ., March 15-17, 1995
alg-geom/9507005

On level lines of a conformal isomorphism of a domain onto the disk
by S.Yu. Orevkov
Mat. Zametki,56(1994), no. 5, 145-148 (in Russian); English transl.: Math. Notes, 56(1994), 1197-1199
pdf (English) (112 K) dvi (English) (15 K) ps.gz (English) (41 K) pdf (Russian) (126 K) ps.gz (Russian) (45 K)

An example in connection with the Jacobian conjecture.
by S.Yu. Orevkov
Mat. Zametki,47(1990), no. 1, 127-136; Erratum: ibid, 49(1991), no. 6, p. 148 (in Russian); pdf (Russian) (1073 K) pdf (erratum, Russian)
English transl.: Math. Notes, 47(1990), 82-88; Erratum: ibid., 49(1991), p.659. pdf (English) (588 K) pdf (erratum, English)
In English translation, some pluses look as minuses because of the quality of copy machine. So, see the Russian version for the definition of P(t) and Q(t) on p. 128.

The fundamental group of the complement of a plane algebraic curve
by S.Yu. Orevkov
Mat. Sbornik,137(179)(1988), no. 2, 260-270 (in Russian); English transl.: Math. USSR Sbornik, 65(1990), no. 1, 267-277
pdf (169 K) ps (346 K) ps.gz (157 K) abstract

On three-sheeted polynomial mappings of C²
by S.Yu. Orevkov
Izvestia AN SSSR. Ser. Mat., 50(1986), no. 6, 1231-1240 (in Russian)
English translation: Math. USSR-Izvestiya, 29(1987), 587-596
Abstract: It is proved that the Jacobian of a 3-fold polynomial mapping of the complex plane into itself cannot be constant, i.e. a counter-example to the Jacobian Conjecture in dimension 2 cannot be realised by a 3-fold mapping
pdf (163 K) ps (348 K) ps.gz 163 K)