A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem
Algebraic Geometry
2007-05-23 v2 Symplectic Geometry
Abstract
The paper is a short supplement of the longer paper "The Algebraic Proof of the Universality Theorem", preprint math.AG/0402045. In this short note, we outline the geometric meaning of Universality theorem (conjecture by Gottsche) as a non-linear extension of surface Riemann-Roch Theorem, inspired by the string theory argument of Yau-Zaslow to probe non-linear information from linear systems of algebraic surfaces. The universality theorem is an existence result which reflects the topological nature of the Riemann-Roch problem. We also outline the crucial role that Yau-Zaslow formula has played in our theory. At the end, we list a few open problems related to the algebraic solution of the problem.
Cite
@article{arxiv.math/0405113,
title = {A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem},
author = {Ai-Ko Liu},
journal= {arXiv preprint arXiv:math/0405113},
year = {2007}
}
Comments
26 pages, a reference is updated