On the cohomology of tautological bundles over Quot schemes of curves

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Marian, Alina, Oprea, Dragos, Sam, Steven V
Natura: Preprint
Pubblicazione: 2022
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866910212419485696
author Marian, Alina
Oprea, Dragos
Sam, Steven V
author_facet Marian, Alina
Oprea, Dragos
Sam, Steven V
contents We consider tautological bundles and their exterior and symmetric powers on the Quot scheme over the projective line. We prove and conjecture several statements regarding the vanishing of their higher cohomology, and we describe their spaces of global sections via tautological constructions. To this end, we make use of the embedding of the Quot scheme as an explicit local complete intersection in the product of two Grassmannians, studied by Strømme. This allows us to construct resolutions with vanishing cohomology for the tautological bundles and their exterior and symmetric powers. We further illustrate our approach with a few additional cohomological calculations.
format Preprint
id arxiv_https___arxiv_org_abs_2211_03901
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On the cohomology of tautological bundles over Quot schemes of curves
Marian, Alina
Oprea, Dragos
Sam, Steven V
Algebraic Geometry
We consider tautological bundles and their exterior and symmetric powers on the Quot scheme over the projective line. We prove and conjecture several statements regarding the vanishing of their higher cohomology, and we describe their spaces of global sections via tautological constructions. To this end, we make use of the embedding of the Quot scheme as an explicit local complete intersection in the product of two Grassmannians, studied by Strømme. This allows us to construct resolutions with vanishing cohomology for the tautological bundles and their exterior and symmetric powers. We further illustrate our approach with a few additional cohomological calculations.
title On the cohomology of tautological bundles over Quot schemes of curves
topic Algebraic Geometry
url https://arxiv.org/abs/2211.03901