Semistablity of syzygy bundles on projective spaces in positive characteristics
| dc.creator | Trivedi, V. | |
| dc.date | 2008-04-03 | |
| dc.date | 2009-04-24 | |
| dc.date.accessioned | 2026-07-07T13:07:27Z | |
| dc.date.available | 2026-07-07T13:07:27Z | |
| dc.description | 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 $\sV_d$ 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.description | 25 pages, new version. Also gives estimate on mu-max, and gives a version of Langer's theorem in all degrees and characteristics | |
| dc.identifier | https://arxiv.org/abs/0804.0547 | |
| dc.identifier | http://arxiv.org/abs/0804.0547 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228097 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L30 | |
| dc.title | Semistablity of syzygy bundles on projective spaces in positive characteristics | |
| dc.type | text |