Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stable pair invariants of surfaces and Seiberg-Witten invariants (1303.5340v3)

Published 21 Mar 2013 in math.AG, hep-th, and math.SG

Abstract: The moduli space of stable pairs on a local surface $X=K_S$ is in general non-compact. The action of $\mathbb{C}*$ on the fibres of $X$ induces an action on the moduli space and the stable pair invariants of $X$ are defined by the virtual localization formula. We study the contribution to these invariants of stable pairs (scheme theoretically) supported in the zero section $S \subset X$. Sometimes there are no other contributions, e.g. when the curve class $\beta$ is irreducible. We relate these surface stable pair invariants to the Poincar\'e invariants of D\"urr-Kabanov-Okonek. The latter are equal to the Seiberg-Witten invariants of $S$ by work of D\"urr-Kabanov-Okonek and Chang-Kiem. We give two applications of our result. (1) For irreducible curve classes the GW/PT correspondence for $X = K_S$ implies Taubes' GW/SW correspondence for $S$. (2) When $p_g(S) = 0$, the difference of surface stable pair invariants in class $\beta$ and $K_S - \beta$ is a universal topological expression.

Summary

We haven't generated a summary for this paper yet.