اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSemistablity of syzygy bundles on projective spaces in positive characteristics
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تأليف
V. Trivedi
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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 $mu_{max}(sV_d^*)$?} Here we prove that (1) the bundle $sV_d$ is semistable, for a certain infinite set of integers $dgeq 0$, and (2) for arbitrary $d$, there is a good enough estimate on $mu_{max}(sV_d^*)$ in terms of $d$ and $n$. In particular one obtains Langers theorem, in arbitrary characeristic.
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