Enumeration of curves with one singular point

JOURNAL OF GEOMETRY AND PHYSICS

卷:104

Article

Basu, Somnath¹  Mukherjee, Ritwik² 

[1] RKM Vivekananda Univ, Dept Math Sci, Wb 711202, India

[2] TIFR, Dept Math, Bombay 400005, Maharashtra, India

关键词: Enumerative geometry;    Euler class;    Transversality;    Singularity;    Vector bundle;   

DOI  :  10.1016/j.geomphys.2016.02.008

来源: Elsevier

【 摘 要 】

In this paper we obtain an explicit formula for the number of curves in P-2, of degree d, passing through (d(d + 3)/2 - k) generic points and having a singularity X, where X is of type A(k <= 7), D-k <= 7 or E-k <= 7. Our method comprises of expressing the enumerative problem as the Euler class of an appropriate bundle and using a purely topological method to compute the degenerate contribution to the Euler class. These numbers have also been computed by M. Kazarian using the existence of universal formulas for Thom polynomials. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free