Poincare invariants are Seiberg-Witten invariants
Huai-liang Chang, Young-Hoon Kiem
TL;DR
This paper proves a conjecture linking Poincare invariants with Seiberg-Witten invariants for smooth projective surfaces using algebraic geometry and virtual cycle techniques.
Contribution
It establishes an algebro-geometric framework for Seiberg-Witten invariants, confirming a conjecture by Durr, Kabanov, and Okonek.
Findings
Proves the conjecture relating Poincare and Seiberg-Witten invariants.
Introduces the use of cosection localization principle in this context.
Provides a unified algebraic approach to Seiberg-Witten invariants.
Abstract
We prove a conjecture of Durr, Kabanov and Okonek which provides an algebro-geometric theory of Seiberg-Witten invariants for all smooth projective surfaces. Our main technique is the cosection localization principle of virtual cycles.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology