Recent publications

Books

• Alex Degtyarev. Topology of Algebraic Curves: An Approach via Dessins d'Enfants. De Gruyter Studies in Mathematics, 44. Walter de Gruyter & Co., Berlin, 2012. xvi+393 pp. ISBN: 978-3-11-025591-1. Current book page [GAP code]
• Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. Real Enriques surfaces. Lecture Notes in Mathematics, 1746. Springer-Verlag, Berlin, 2000. xvi+259 pp. ISBN: 3-540-41088-0. Table of Contents

Ph.D. thesis

• Alex Degtyarev. Topology of complex plane projective algebraic curves (in Russian). Steklov Math. Inst., Leningrad Branch (LOMI), Leningrad, 1987.

Private notes

• Alex Degtyarev. The Bertini involution (after Ethel I. Moody). [Maple implementation]
• Alex Degtyarev. Maximizing plane sextics with double points. Machine readable form: [code] Updated [October 8, 2013]: due to S. Orevkov, the equations of all irreducible maximizing sextics with A-type singularities only are known now, see Parametric equations of plane sextic curves with a maximal set of double points.

Papers

• Alex Degtyarev. Conics on smooth quartic surfaces (submitted). [Companion text (algorithms/tables)]; Current version
• Alex Degtyarev, Ilia Itenberg. Real plane sextics without real points (submitted). Current version
• Alex Degtyarev, Sławomir Rams. Lines on $K3$-quartics via triangular sets Discrete Comput. Geom. (2024). Current version
• Alex Degtyarev, Sławomir Rams. Counting Lines with Vinberg's algorithm (submitted). [Extended Fano graphs]; Current version
• Alex Degtyarev. Conics on Barth--Bauer octics. Science China Math. 67 (2024), no. 7, 1507--1524. Current version
• Alex Degtyarev, Ilia Itenberg, John Christian Ottem. Planes in cubic fourfolds. Algebraic Geometry 10 (2023), no. 2, 228--258. Current version
• Alex Degtyarev, Vincent Florens, Ana G. Lecuona. Slopes and concordance of links. Algebraic & Geometric Topology, 24 (2024), no. 2, 1101--1120 Current version
• Alex Degtyarev. Conics on Kummer quartics. Tohoku Mathematical Journal, 75 (2023), no. 3, 395--421. [Complete tables]; Current version
• Alex Degtyarev, Vincent Florens, Ana G. Lecuona. Slopes and signatures of links. Fundamenta Matematicae, 258 (2022), 65--114. Current version
• Alex Degtyarev. Tritangents to smooth sextic curves. Annales de l'Institut Fourier, 72 (2022), 2299–2338. Current version [Full version is available as MPIM preprint or here]
• Alex Degtyarev. Lines in supersingular quartics. J. Math. Soc. Japan, 74 (2022), 973–1019. Current version
• Alex Degtyarev. Conics on sextic $K3$-surfaces in $P^4$. Nagoya Math. J., 246 (2022), 273-304. Current version
• Alex Degtyarev. 800 conics on a smooth quartic surface. Journal of Pure and Applied Algebra, 226 (2022), 107077. Current version
• Alex Degtyarev, Vincent Florens, Ana G. Lecuona. Slopes of links and signature formulas. Topology, geometry, and dynamics—V. A. Rokhlin-Memorial, 93–105, Contemp. Math., vol. 772, Amer. Math. Soc., Providence, RI, 2021. Current version
• Alex Degtyarev. Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin: “Singular Algebraic Curves” (book review). Jahresbericht der Deutschen Mathematiker-Vereinigung, 123:2 (2021), 131--135. Publisher's shared link; doi:10.1365/s13291-021-00226-4
• Erwan Brugallé, Alex Degtyarev, Ilia Itenberg, Frédéric Mangolte. Real algebraic curves with large finite number of real points. European J. Math. 5:3 (2019), 686--711. Current version; doi:10.1007/s40879-019-00324-9
• Alex Degtyarev. Lines on smooth polarized $K3$-surfaces. Discrete Comput. Geom. 62:3 (2019), 601--648. Current version [Fano graphs]; doi:10.1007/s00454-018-0038-5
• Alex Degtyarev. Smooth models of singular $K3$-surfaces. Rev. Mat. Iberoam. 35:1 (2019), 125--172. Current version [test matrices]; doi:10.4171/rmi/1051
• Alex Degtyarev, Ilia Itenberg, Ali Sinan Sertoz. Lines on quartic surfaces. Math. Ann. 368:1 (2017), 753--809. Current version; doi:10.1007/s00208-016-1484-0
• Alex Degtyarev. Projective spaces in Fermat varieties. Proc. Kinosaki Symp. on Algebraic Geometry, Kyoto Univ., 2015, pp. 81--95. Current version
• Alex Degtyarev, Vincent Florens, Ana G. Lecuona. The signature of a splice. Int. Math. Res. Not. IMRN 8 (2017), 2249--2283. Current version; doi:10.1093/imrn/rnw068
• Alex Degtyarev, Ichiro Shimada. On the topology of projective subspaces in complex Fermat varieties. J. Math. Soc. Japan 68:3 (2016), 975--996. Current version
• Alex Degtyarev. On the Néron–Severi lattice of a Delsarte surface. Kyoto J. Math. 56:3 (2016), 611--632. Current version
• Aysegul Akyol, Alex Degtyarev. Geography of irreducible plane sextics. Proc. London Math. Soc. (3) 111 (2015), 1307--1337. Current version; doi:10.1112/plms/pdv053
• Alex Degtyarev. Lines generate the Picard groups of certain Fermat surfaces. J. Number Theory, 147 (2015), 454--477. Current version; doi:10.1016/j.jnt.2014.07.020
• Alex Degtyarev. The Alexander module of a trigonal curve. II. Singularities in geometry and topology 2011, Adv. Stud. Pure Math., 66, Math. Soc. Japan, Tokyo, 2015, pp. 47--69. Current version
• Alex Degtyarev. On the Artal--Carmona--Cogolludo construction. J. Knot Theory Ramifications 23:5 (2014), 1450028 (35 pages). Current version [details] [code]; doi:10.1142/S021821651450028X
• Alex Degtyarev, Ilia Itenberg, Victor Zvonilov. Real trigonal curves and real elliptic surfaces of type I. J. Reine Angew. Math. 686 (2014), 221--246. Current version
• Alex Degtyarev. The Alexander module of a trigonal curve. Rev. Mat. Iberoam. 30:1 (2014), 25--64. Current version; doi:10.4171/RMI/768
• Alex Degtyarev. On plane sextics with double singular points. Pacific J. Math. 265:2 (2013), 327--348. Current version [GAP code]; doi:10.2140/pjm.2013.265.327
• Alex Degtyarev, Nermin Salepci. Products of pairs of Dehn twists and maximal real Lefschetz fibrations. Nagoya Math. J. 210 (2013), 83--132. Current version; doi:10.1215/00277630-2077026
• Alex Degtyarev. Dihedral coverings of trigonal curves. Indiana Univ. Math. J. 61:3 (2012), 901--938. Current version; doi:10.1512/iumj.2012.61.4607
• Alex Degtyarev. Towards the generalized Shapiro and Shapiro conjecture. Perspectives in analysis, geometry, and topology, Progr. Math., 296, Birkhäuser/Springer, New York, 2012, pp. 67--79 Current version
• Alex Degtyarev. Transcendental lattice of an extremal elliptic surface. J. Algeb. Geom., 21 (2012), 413--444. Current version
• Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. On the number of components of a complete intersection of real quadrics. Perspectives in analysis, geometry, and topology, Progr. Math., 296, Birkhäuser/Springer, New York, 2012, pp. 81--107 Current version
• Alex Degtyarev. Hurwitz equivalence of braid monodromies and extremal elliptic surfaces. Proc. London Math. Soc. (3) 103 (2011), 1083--1120. Current version; doi:10.1112/plms/pdr013
• Alex Degtyarev. The fundamental group of a generalized trigonal curve. Osaka J. Math., 48:3 (2011), 749--782. Current version
• Alex Degtyarev. Plane sextics with a type E₆ singular point. Michigan Math. J., 60 (2011), 243--269. Current version
• Alex Degtyarev. Topology of plane algebraic curves: the algebraic approach. The Proceedings of LIB60BER Conference, Contemp. Math., 538 (2011), 137--161 Current version
• Alex Degtyarev. Classical Zariski pairs. J. Singularities, 2 (2010), 51--55 Current version
• Alex Degtyarev. Plane sextics with a type E₈ singular point. Tohoku Math. J., 62:3 (2010), 329--355. Current version
• Alex Degtyarev, Ilia Itenberg. On real determinantal quartics. Proceedings of the Gökova Geometry--Topology Conference 2010, Int. Press, Somerville, MA, pp. 110--128. Current version
• Alex Degtyarev. Plane sextics via dessins d'enfants. Geometry & Topology, 14:1 (2010), 393--433. Current version; doi:10.2140/gt.2010.14.393
• Alex Degtyarev. Fundamental groups of symmetric sextics. II. Proc. London Math. Soc., 99:2 (2009), 353--385. Current version; doi:10.1112/plms/pdp003
• Alex Degtyarev. Irreducible plane sextics with large fundamental groups. J. Math. Soc. Japan, 61:4 (2009), 1131--1169. Current version
• Alex Degtyarev. On irreducible sextics with non-abelian fundamental group. Proceedings of Niigata--Toyama Conferences 2007, Adv. Stud. Pure Math. 56 (2009), 65--92. Current version
• Alex Degtyarev, Mutsuo Oka. A plane sextic with finite fundamental group. Proceedings of Niigata--Toyama Conferences 2007, Adv. Stud. Pure Math. 56 (2009), 93--108. Current version
• Alex Degtyarev. Zariski k-plets via dessins d'enfants. Comment. Math. Helv., 84:3 (2009), 639--671. Current version
• Alex Degtyarev. Oka's conjecture on irreducible plane sextics. II. J. Knot Theory Ramifications 18:8 (2009), 1065-1080. Current version; doi:10.1142/S0218216509007348
• Alex Degtyarev. Fundamental groups of symmetric sextics. J. Math. Kyoto Univ., 48:4 (2008), 765--792. Current version. Reference ID: JMKU0480404
• Alex Degtyarev. Stable symmetries of plane sextics. Geometriæ Dedicata, 137:1 (2008), 199--218. Current version. The original publication is available at www.springerlink.com; doi:10.1007/s10711-008-9293-6
• Alex Degtyarev. Oka's conjecture on irreducible plane sextics. J. London Math. Soc., 78:2 (2008), 329--351. Current version; doi:10.1112/jlms/jdn029
• Alex Degtyarev. On deformations of singular plane sextics. J. Algeb. Geom. 17 (2008), 101--135. Current version
• Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. On deformation types of real elliptic surfaces. Amer. J. Math., 130:6 (2008), 1561--1627. Current version; doi:10.1353/ajm.0.0029
• Alex Degtyarev, Torsten Ekedahl, Ilia Itenberg, Boris Shapiro, Michael Shapiro. On total reality of meromorphic functions. Ann. Inst. Fourier 57:5 (2007), 2015-2030. Current version
• Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. Deformation Finiteness for Real Hyperkähler Manifolds. Moscow Math. J. 7:2 (2007), 257--263, 350 Current version
• Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. Finiteness and quasi-simplicity for symmetric $K3$-surfaces. Duke Math. J. 122:1 (2004), 1--49. Current version
• Alex Degtyarev, Viatcheslav Kharlamov. Real rational surfaces are quasi-simple. J. Reine Angew. Math. 551 (2002), 87--99. Current version
• Alex Degtyarev. A divisibility theorem for the Alexander polynomial of a plane algebraic curve. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 280 (2001), Geom. i Topol. 7, 146--156, 300; translation in J. Math. Sci. (N. Y.) 119:2 (2004), 205--210. Current version
• Alex Degtyarev, Viatcheslav Kharlamov. Topological properties of real algebraic varieties: du côté de chez Rokhlin. Uspekhi matematicheskikh nauk. No. 2, 2000. Engl. transl. in Russian mathematical surveys. Current version available here
• Alex Degtyarev. Quintics in $Cp^2$ with nonabelian fundamental group. Algebra i Analiz. 11:5 (1999), 130--151. Engl. transl. in St. Petersburg Math. J., 11:5 (2000) or here
• Alex Degtyarev, Victor Zvonilov. Rigid isotopy classification of real algebraic curves of bidegree $(3,3)$ on quadrics. Matematicheskie zametki, December 1999. Engl. transl. in Mathematical notes. Current version
• Alex Degtyarev. On the Pontrjagin-Viro form. Advances Math. Sciences, Rokhlin's Memorial volume. Currently available from alg-geom@eprints.math.duke.edu via get 9705011 or here
• Alex Degtyarev, Viatcheslav Kharlamov. Empty real Enriques surfaces and Enriques-Einstein-Hitchin 4-manifolds Appearing in Fields Institute Communications. Currently available from alg-geom@eprints.math.duke.edu via get 9704003, or from AmS server, or here
• Alex Degtyarev, Viatcheslav Kharlamov. On the moduli space of real Enriques surfaces, C.R. Acad. Sci. Paris Ser I, 1997, no. 3. Available here
• Alex Degtyarev, Viatcheslav Kharlamov. Around real Enriques surfaces. Proc. Int. Conference on Real Algebrtaic Geometry in Segovia, Revista Matematica de la Universidad Complutense de Madrid, 10 (1997), 93-109. Available here
• Alex Degtyarev, Viatcheslav Kharlamov. Halves of a real enriques surface. Comm. Math. Helv., 71:4 (1996), 628-663. Extended version: Distribution of the components of a real Enriques surface. Preprint of the Max-Planck Institute, MPI/95-58 (1995); also available from AMS server as AMSPPS # 199507-14-005 or here
• Alex Degtyarev, Viatcheslav Kharlamov. Topological classification of real Enriques surfaces. Topology, 35:3 (1996), 711-729. Available here
• Alex Degtyarev. Quadratic transformations Rp2 --> Rp2. In: Topology of Real Algebraic Varieties and Related Topics, Amer. Math. Soc. Transl. (2), 173 (1996), 61-73. Available here
• Alex Degtyarev. Alexander polynomial of a curve of degree 6. J. Knot Theory Ramif., 3 (1994), 439-454. Available here

Last update: November 2, 2009