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Main Author: Ito, Atsushi
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.01335
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author Ito, Atsushi
author_facet Ito, Atsushi
contents For a locally free sheaf $\mathcal{E}$ on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of $\mathcal{E}$ of length $n$ supported at a fixed point. It is known that the punctual Quot scheme is a normal projective variety with canonical Gorenstein singularities. In this note, we show that the punctual Quot scheme is a $\mathbb{Q}$-factorial Fano variety of Picard number one.
format Preprint
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institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A remark on some punctual Quot schemes on smooth projective curves
Ito, Atsushi
Algebraic Geometry
For a locally free sheaf $\mathcal{E}$ on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of $\mathcal{E}$ of length $n$ supported at a fixed point. It is known that the punctual Quot scheme is a normal projective variety with canonical Gorenstein singularities. In this note, we show that the punctual Quot scheme is a $\mathbb{Q}$-factorial Fano variety of Picard number one.
title A remark on some punctual Quot schemes on smooth projective curves
topic Algebraic Geometry
url https://arxiv.org/abs/2504.01335