Genus-Zero Mirror Principle For Two Marked Points

TL;DR

This paper extends the genus-zero mirror principle to two marked points, providing explicit hypergeometric class descriptions and applications to Euler classes of obstruction bundles, advancing the understanding of mirror symmetry in enumerative geometry.

Contribution

It generalizes the genus-zero mirror principle to two marked points, explicitly identifying the data in terms of hypergeometric classes and establishing a foundation for the general case.

Findings

Explicit hypergeometric class descriptions for two marked points

Extension of mirror principle to genus zero with two markings

Applications to Euler classes of obstruction bundles

Abstract

We study a generalization of Lian-Liu-Yau's notion of Euler data in genus zero and show that certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli with markings induce data satisfying the generalization. In the case of one or two markings, this data is explicitly identified in terms of hypergeometric type classes, constituting a complete extension of Lian-Liu-Yau's mirror principle in genus zero to the case of two marked points and establishing a program for the general case. We give several applications involving the Euler class of obstruction bundles induced by a concavex bundle on $P^n$.