2008/04/03 by V. Trivedi, Trivedi, V.
Mathematics · #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30
paper · pdf · doi:10.48550/arxiv.0804.0547
25 pages, new version. Also gives estimate on mu-max, and gives a version of Langer's theorem in all degrees and characteristics
arxiv created 2009/04/24 · arxiv updated 2009/12/01
In 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 \sVd of \mathcal O(d), is \sVd semistable for arbitrary n, d and p = char k?, or is there a good estimate on μmax(\sVd^*)? Here we prove that (1) the bundle \sVd is semistable, for a certain infinite set of integers d≥ 0, and (2) for arbitrary d, there is a good enough estimate on μmax(\sVd^*) in terms of d and n. In particular one obtains Langer's theorem, in arbitrary characeristic.