Semistability of syzygy bundles on projective spaces in positive characteristics

V. Trivedi

doi:10.1142/S0129167X10006598

Semistability of syzygy bundles on projective spaces in positive characteristics

V. Trivedi

Mathematics

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9 Scopus citations

Abstract

We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, V_d, of the line bundle O(d) over P_kⁿ is semistable, for a certain infinite set of integers d < 0. Moreover, for arbitrary d, there is a "good enough estimate" on mu_max(V_d*) $ in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.

Original language	English
Pages (from-to)	1475-1504
Number of pages	30
Journal	International Journal of Mathematics
Volume	21
Issue number	11
DOIs	https://doi.org/10.1142/S0129167X10006598
State	Published - Nov 2010

Keywords

general hypersurface
GL(n + 1)-bundles
p-adic expansion
restriction theorem
Semistable sheaves
syzygy bundle

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abstract = "We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, Vd, of the line bundle O(d) over Pkn is semistable, for a certain infinite set of integers d < 0. Moreover, for arbitrary d, there is a {"}good enough estimate{"} on mumax(Vd*) \$ in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.",

keywords = "general hypersurface, GL(n + 1)-bundles, p-adic expansion, restriction theorem, Semistable sheaves, syzygy bundle",

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T1 - Semistability of syzygy bundles on projective spaces in positive characteristics

AU - Trivedi, V.

PY - 2010/11

Y1 - 2010/11

N2 - We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, Vd, of the line bundle O(d) over Pkn is semistable, for a certain infinite set of integers d < 0. Moreover, for arbitrary d, there is a "good enough estimate" on mumax(Vd*) $ in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.

AB - We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, Vd, of the line bundle O(d) over Pkn is semistable, for a certain infinite set of integers d < 0. Moreover, for arbitrary d, there is a "good enough estimate" on mumax(Vd*) $ in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.

KW - general hypersurface

KW - GL(n + 1)-bundles

KW - p-adic expansion

KW - restriction theorem

KW - Semistable sheaves

KW - syzygy bundle

UR - https://www.scopus.com/pages/publications/78649268607

U2 - 10.1142/S0129167X10006598

DO - 10.1142/S0129167X10006598

M3 - Article

AN - SCOPUS:78649268607

SN - 0129-167X

VL - 21

SP - 1475

EP - 1504

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 11

ER -

Semistability of syzygy bundles on projective spaces in positive characteristics

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