Splitting of supervector bundles on projective superspaces

Fuente: arXiv
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Main Authors: Almeida, Charles, Bruzzo, Ugo
Format: Preprint
Published: 2025
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author Almeida, Charles
Bruzzo, Ugo
author_facet Almeida, Charles
Bruzzo, Ugo
contents We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that $n \geq 2$. For $n=1$ we provide an example of a supervector bundle that cannot be written as a sum of line bundles.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10765
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Splitting of supervector bundles on projective superspaces
Almeida, Charles
Bruzzo, Ugo
Algebraic Geometry
14M30, 14F06, 14F17
We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that $n \geq 2$. For $n=1$ we provide an example of a supervector bundle that cannot be written as a sum of line bundles.
title Splitting of supervector bundles on projective superspaces
topic Algebraic Geometry
14M30, 14F06, 14F17
url https://arxiv.org/abs/2501.10765