A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem

Details A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem A Note About Universality Theorem as an Enumerative Riemann-Roch Theorem

2004-05-06

arxiv.org/abs/math/0405113v2

Mathematics

Algebraic Geometry

26 pages, a reference is updated

Scientific paper

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.

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