Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves

Andreas Krug

doi:10.48550/arXiv.2305.17124

Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves

Andreas Krug

Institute of Algebraic Geometry

Research output: Contribution to journal › Article › Research › peer review

Abstract

We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles.

Original language	English
Article number	103600
Number of pages	30
Journal	Journal des Mathematiques Pures et Appliquees
Volume	189
E-pub ahead of print	25 Jul 2024
DOIs	https://doi.org/10.48550/arXiv.2305.17124 https://doi.org/10.1016/j.matpur.2024.103600
Publication status	Published - Sept 2024

Keywords

math.AG
Fourier–Mukai transforms
Sheaf cohomology
Tautological bundles
Punctual Quot schemes

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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10.48550/arXiv.2305.17124Licence: Arxiv nonexclusive-distrib 1.0
10.1016/j.matpur.2024.103600Licence: CC BY 4.0

Cite this

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abstract = " We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles. ",

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N2 - We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles.

AB - We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of the original vector bundle on the curve. We also give a vanishing result for the push-forward along the Quot--Chow morphism of tensor and wedge products of duals of tautological bundles.

KW - math.AG

KW - Fourier–Mukai transforms

KW - Sheaf cohomology

KW - Tautological bundles

KW - Punctual Quot schemes

UR - https://www.scopus.com/pages/publications/85200645387

U2 - 10.48550/arXiv.2305.17124

DO - 10.48550/arXiv.2305.17124

M3 - Article

SN - 0021-7824

VL - 189

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

M1 - 103600

ER -

Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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