Quillen-type bundle and geometric prequantization on moduli space of the Seiberg-Witten equations on product of Riemann surfaces

2022/03/30 by Rukmini Dey, Dey, Rukmini
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.DG #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.2203.15997

6pages

arxiv created 2022/03/30 · openalex publication_date 2022/03/30 · arxiv updated 2022/03/31 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on Σ× Σ where Σ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type determinant line bundle on it and show its curvature is proportional to the symplectic form.

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