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DESCRIPTION: Abstract: We know that a Frobenius pull back of a semistable
bundle need not remain semistable. However\, if X is a nonsingular projecti
ve curve of genus g and defined over a field of characterstic p >\; 0\, t
hen Shepherd-Barron and X. Sun proved (independently)\, that for a semistab
le vector bundle V of rank r\, the instability degree of F * V is bounded b
y 2(g-1)(r-1). This bound on the instability is useful in keeping a chec
k on some of the behaviour of a vector bundle afterFrobenius pullbacks. F
or example one can prove that\, for any vector bundle V and for large p (i
n terms of degree of X and rank of V)\, the Harder-Narasimhan filtration of
F * V is a refinement of the Frobenius pull back of the Harder-Narasimhan
filtration of V.We give counterexamples to prove that some such conditions
on p is necessary. We extend such results to vector bundles over highe
r dimesional verieties.To prove these\, we answer a question/conjecture of
X. Sun (though for p bigger than rank of E + dimension of X)\, which is an
anaolgue of the above mentioned result of Shepherd-Barron and X. Sun in
higher dimension.
DTSTAMP:20140108T112700
DTSTART:20140116T171500
CLASS:PUBLIC
LOCATION:Hörsaal 1\, Arnimallee 3
SEQUENCE:0
SUMMARY:Mathe. Kolloquium: Dr. Vijaya Trivedi (Mumbai / Berlin)
UID:33640897@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/math/dates/colloquium/Archiv-2014/16_01_14T
rivedi.html
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