Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications

2021/01/06 by Xueqing Wen, Wen, Xueqing
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2101.01913

openalex publication_date 2021/01/06 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on ℙ¹ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the Littlewood-Richardson coefficients from the Verlinde formula, and solve the nilpotent case of the Deligne-Simpson problem via geometric methods.

Citations

• Lectures on Nakajima's Quiver Varieties
• Globally F-regular type of moduli spaces and Verlinde formula
• Parabolic Hitchin Maps and Their Generic Fibers

Related

• Relative spectral correspondence for parabolic Higgs bundles and Deligne--Simpson problem
• Integrable systems and Torelli theorems for the moduli spaces of\n parabolic bundles and parabolic Higgs bundles
• Higgs bundles and indecomposable parabolic bundles over the projective line
• Moduli of Higgs bundles over the five punctured sphere
• The moduli stack of parabolic bundles over the projective line, quiver\n representations, and the Deligne-Simpson problem