Tangency quantum cohomology and characteristic numbers

Anais da Academia Brasileira de Ciências

Joachim Kock¹ 

[1] ,Universidade Federal de Pernambuco Departamento de Matemática Recife PE ,Brasil

关键词: Enumerative geometry;    characteristic numbers;    quantum cohomology;    Gromov-Witten invariants;    geometria enumerativa;    números característicos;    co-homologia quântica;    invariantes Gromov-Witten;   

DOI  :  10.1590/S0001-37652001000300002

来源: SciELO

【 摘 要 】

This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde. In both cases, however, the background metric is not the usual Poincaré metric but a certain deformation of it, which surprisingly encodes all the combinatorics of the peculiar way modified psi classes restrict to the boundary. This machinery is applied to various enumerative problems, among which characteristic numbers in any projective homogeneous variety, characteristic numbers for curves with cusp, prescribed triple contact, or double points.

【 授权许可】

CC BY   
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