Cohomological Characterization of Vector Bundles on Grassmannians of Lines
Enrique Arrondo, Francesco Malaspina
TL;DR
This paper introduces a new regularity concept for sheaves on Grassmannians of lines, extending criteria for line bundle characterization and providing cohomological descriptions of universal bundle powers.
Contribution
It develops a regularity notion for sheaves on Grassmannians and extends Evans-Griffith criterion to characterize direct sums of line bundles.
Findings
Extended Evans-Griffith criterion for Grassmannians
Cohomological characterization of universal bundle powers
New regularity notion for coherent sheaves
Abstract
We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory