Semistablity of syzygy bundles on projective spaces in positive characteristics

dc.creatorTrivedi, V.
dc.date2008-04-03
dc.date2009-04-24
dc.date.accessioned2026-07-07T13:07:27Z
dc.date.available2026-07-07T13:07:27Z
dc.descriptionIn char $k = p >0$, A. Langer proved a strong restriction theorem (in the style of H. Flenner) for semistable sheaves to a very general hypersurface of degree $d$, on certain varieties, with the condition that `char $k > d$'. He remarked that to remove this condition, it is enough to answer either of the following questions affirmatively: {\it For the syzygy bundle $\sV_d$ of ${\mathcal O}(d)$, is $\sV_d$ semistable for arbitrary $n, d$ and $p = {char} k$?, or is there a good estimate on $μ_{max}(\sV_d^*)$?} Here we prove that (1) the bundle $\sV_d$ is semistable, for a certain infinite set of integers $d\geq 0$, and (2) for arbitrary $d$, there is a good enough estimate on $μ_{max}(\sV_d^*)$ in terms of $d$ and $n$. In particular one obtains Langer's theorem, in arbitrary characeristic.
dc.description25 pages, new version. Also gives estimate on mu-max, and gives a version of Langer's theorem in all degrees and characteristics
dc.identifierhttps://arxiv.org/abs/0804.0547
dc.identifierhttp://arxiv.org/abs/0804.0547
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228097
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14L30
dc.titleSemistablity of syzygy bundles on projective spaces in positive characteristics
dc.typetext

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