Complex planar curves homeomorphic to a line have at most four singular points

Journal de Mathématiques Pures et Appliquées - Tập 158 - Trang 144-182 - 2022
Mariusz Koras1, Karol Palka2
1Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
2Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland

Tài liệu tham khảo

Artal Bartolo, 2006, Superisolated Surface Singularities, Singularities and Computer Algebra, vol. 324, 13 Abhyankar, 1973, Newton-Puiseux expansion and generalized Tschirnhausen transformation. I, II, J. Reine Angew. Math., 260, 47 Abhyankar, 1973, J. Reine Angew. Math., 261, 29 Baranowski, 2016, Heegaard-Floer homologies and rational cuspidal curves, Lecture Notes, vol. 3 Borodzik, 2019, Involutive Heegaard-Floer homology and rational cuspidal curves, Proc. Lond. Math. Soc., 118, 441, 10.1112/plms.12179 Borodzik, 2014, Heegaard-Floer homology and rational cuspidal curves, Forum Math. Sigma, 2 Borodzik, 2016, Semigroups, d-invariants and deformations of cuspidal singular points of plane curves, J. Lond. Math. Soc. (2), 93, 439, 10.1112/jlms/jdv068 Bodnár, 2016, Lattice cohomology and rational cuspidal curves, Math. Res. Lett., 23, 339, 10.4310/MRL.2016.v23.n2.a3 Bodnár Borodzik, 2010, Complex algebraic plane curves via Poincaré-Hopf formula. II. Annuli, Isr. J. Math., 175, 301, 10.1007/s11856-010-0013-1 Cassou-Nogues, 2009, Closed embeddings of C⁎ in C2. I, J. Algebra, 322, 2950, 10.1016/j.jalgebra.2008.11.013 Drucker, 1979, Graphical evaluation of sparse determinants, Proc. Am. Math. Soc., 77, 35, 10.1090/S0002-9939-1979-0539626-2 Dimca, 2017, Free divisors and rational cuspidal plane curves, Math. Res. Lett., 24, 1023, 10.4310/MRL.2017.v24.n4.a5 Dimca, 2018, Free and nearly free curves vs. rational cuspidal plane curves, Publ. Res. Inst. Math. Sci., 54, 163, 10.4171/PRIMS/54-1-6 Dimca, 2018, On the freeness of rational cuspidal plane curves, Mosc. Math. J., 18, 659 Fernández de Bobadilla, 2006, On rational cuspidal projective plane curves, Proc. Lond. Math. Soc., 92, 99, 10.1017/S0024611505015467 Fernández de Bobadilla, 2007, Classification of rational unicuspidal projective curves whose singularities have one Puiseux pair, 31 Fernández de Bobadilla, 2007, On rational cuspidal plane curves, open surfaces and local singularities, 411 Fenske, 1999, Rational 1- and 2-cuspidal plane curves, Beitr. Algebra Geom., 40, 309 Fenske, 1999, Rational cuspidal plane curves of type (d,d−4) with χ(ΘV〈D〉)⩽0, Manuscr. Math., 98, 511, 10.1007/s002290050158 Fujita, 1982, On the topology of noncomplete algebraic surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 29, 503 Flenner, 1996, On a class of rational cuspidal plane curves, Manuscr. Math., 89, 439, 10.1007/BF02567528 Flenner, 2000, Rational cuspidal plane curves of type (d,d−3), Math. Nachr., 210, 93, 10.1002/(SICI)1522-2616(200002)210:1<93::AID-MANA93>3.0.CO;2-4 Vasant Gurjar Gurjar, 1996, On contractible curves in the complex affine plane, Tohoku Math. J. (2), 48, 459, 10.2748/tmj/1178225344 Kashiwara, 1987, Fonctions rationnelles de type (0,1) sur le plan projectif complexe, Osaka J. Math., 24, 521 Kollár Kollár, 1998, Birational Geometry of Algebraic Varieties, vol. 134 Koras, 2017, The Coolidge–Nagata conjecture, Duke Math. J., 166, 1, 10.1215/00127094-2017-0010 Koras, 1999, C⁎-actions on C3: the smooth locus of the quotient is not of hyperbolic type, J. Algebraic Geom., 8, 603 Liu, 2014 Luengo, 1987, The μ-constant stratum is not smooth, Invent. Math., 90, 139, 10.1007/BF01389034 Luengo-Velasco, 2005, Links and analytic invariants of superisolated singularities, J. Algebraic Geom., 14, 543, 10.1090/S1056-3911-05-00397-8 Matsuki, 2002, Introduction to the Mori Program, 10.1007/978-1-4757-5602-9 Miyanishi, 2001, Open Algebraic Surfaces, vol. 12 Mohan Kumar, 1982, Curves with negative self-intersection on rational surfaces, J. Math. Kyoto Univ., 22, 767 Matsuoka, 1989, The degree of rational cuspidal curves, Math. Ann., 285, 233, 10.1007/BF01443516 Miyanishi, 1992, Absence of the affine lines on the homology planes of general type, J. Math. Kyoto Univ., 32, 443 Namba, 1984, Geometry of Projective Algebraic Curves Orevkov, 2002, On rational cuspidal curves, Math. Ann., 324, 657, 10.1007/s002080000191 Palka, 2011, Recent progress in the geometry of Q-acyclic surfaces, vol. 54, 271 Palka, 2014, The Coolidge–Nagata conjecture, part I, Adv. Math., 267, 1, 10.1016/j.aim.2014.07.038 Palka, 2015, A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki, J. Algebra Appl., 14 Palka, 2019, Cuspidal curves, minimal models and Zaidenberg's finiteness conjecture, J. Reine Angew. Math., 747, 147, 10.1515/crelle-2016-0021 Piontkowski, 2007, On the number of cusps of rational cuspidal plane curves, Exp. Math., 16, 251, 10.1080/10586458.2007.10128996 Palka, 2017, Classification of planar rational cuspidal curves I. C⁎⁎-fibrations, Proc. Lond. Math. Soc. (3), 115, 638, 10.1112/plms.12049 Palka, 2020, Classification of planar rational cuspidal curves. II. Log del Pezzo models, Proc. Lond. Math. Soc. (3), 120, 642, 10.1112/plms.12300 Russell, 1980, Hamburger-Noether expansions and approximate roots of polynomials, Manuscr. Math., 31, 25, 10.1007/BF01303268 Russell, 2002, Some formal aspects of the theorems of Mumford-Ramanujam, vol. 16, 557 Suzuki, 1974, Propriétés topologiques des polynômes de deux variables, complexes, et automorphismes algébriques de l'espace C2, J. Math. Soc. Jpn., 26, 241, 10.2969/jmsj/02620241 Tono, 2000, Defining equations of certain rational cuspidal curves. I, Manuscr. Math., 103, 47, 10.1007/s002290070028 Tono, 2001, Rational unicuspidal plane curves with κ¯=1, 82 Tono, 2005, On the number of the cusps of cuspidal plane curves, Math. Nachr., 278, 216, 10.1002/mana.200310236 Tono Wakabayashi, 1978, On the logarithmic Kodaira dimension of the complement of a curve in P2, Proc. Jpn. Acad., Ser. A, Math. Sci., 54, 157, 10.3792/pjaa.54.157 Yoshihara, 1988, Plane curves whose singular points are cusps, Proc. Am. Math. Soc., 103, 737, 10.1090/S0002-9939-1988-0947648-8 Zaidenberg, 1983, An irreducible, simply connected algebraic curve in C2 is equivalent to a quasihomogeneous curve, Dokl. Akad. Nauk SSSR, 271, 1048 Zaidenberg, 1995, On the number of singular points of plane curves, 156 Zaidenberg, 1996, On rigid rational cuspidal plane curves, Usp. Mat. Nauk, 51, 149