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arXiv · 1703.07753

Quot schemes and Ricci semipositivity

Indranil Biswas·Harish Seshadri
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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 ${\mathcal O}^{\oplus r}_X$ 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 K\"ahler metric whose Ricci curvature is semipositive.

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Indranil Biswas, Harish Seshadri. 2017-03-22. Quot schemes and Ricci semipositivity. https://arxiv.org/abs/1703.07753

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