Quot schemes and Ricci semipositivity

2017/03/22 by Indranil Biswas, Harish Seshadri, Biswas, Indranil +1
Mathematics · #14H60 #14H81 #32Q10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1703.07753

openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a compact connected Riemann surface of genus at least two, and let \mathcal Q_X(r,d) be the quot scheme that parametrizes all the torsion coherent quotients of \mathcal O^{⊕ r}_X of degree d. This \mathcal Q_X(r,d) is also a moduli space of vortices on X. Its geometric properties have been extensively studied. Here we prove that the anticanonical line bundle of \mathcal Q_X(r,d) is not nef. Equivalently, \mathcal Q_X(r,d) does not admit any Kähler metric whose Ricci curvature is semipositive.

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