Slopes of vector bundles on projective curves and applications to tight closure problems

DOI10.1090/S0002-9947-03-03391-9zbMath1041.13002arXivmath/0302230OpenAlexW1890353761MaRDI QIDQ4429751

Holger Brenner

Publication date: 28 September 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0302230

zbMATH Keywords

tight closurevanishing theoremsprojective bundleslocally free sheaves on smooth projective curvesslopes of bundlesstandard graded rings

Mathematics Subject Classification ID

Vanishing theorems in algebraic geometry (14F17) Graded rings (13A02) Vector bundles on curves and their moduli (14H60) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

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Tight closure and strongly F-regular rings ⋮ Unnamed Item ⋮ New constructions of nef classes on self-products of curves ⋮ Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata ⋮ Tight closure and projective bundles. ⋮ Seshadri constants for vector bundles ⋮ Maximally Frobenius-destabilized vector bundles over smooth algebraic curves ⋮ There is no Bogomolov type restriction theorem for strong semistability in positive characteristic ⋮ Tight closure does not commute with localization ⋮ A linear bound for Frobenius powers and an inclusion bound for tight closure ⋮ Computing the tight closure in dimension two ⋮ On the arithmetic of tight closure ⋮ On nef and semistable Hermitian lattices, and their behaviour under tensor product ⋮ Dagger closure and solid closure in graded dimension two

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