Abstract: We know that a Frobenius pull back of a semistable bundle need not remain semistable. However, if X is a nonsingular projective curve of genus g and defined over a field of characterstic p > 0, then Shepherd-Barron and X. Sun proved (independently), that for a semistable vector bundle V of rank r, the instability degree of F * V is bounded by 2(g-1)(r-1). This bound on the instability is useful in keeping a check on some of the behaviour of a vector bundle afterFrobenius pullbacks. For example one can prove that, for any vector bundle V and for large p (in 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 higher 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.

Ort: Hörsaal 1, Arnimallee 3

16.01.2014 | 17:15

Fachbereich Mathematik und Informatik

Institut für Mathematik

Archive 2014

Mathe. Kolloquium: Prof. Kang Zuo (Mainz)

Mathe. Kolloquium Prof. Holger Brenner (Osnabrück)

Mathe. Kolloquium: Prof. Anina Mischau (FU Berlin)

Mathe. Kolloquium: Dr. Jean-Baptiste Teyssier (FU Berlin)

Vortrag: Dr. Christian Lehn (Paris 7)

Vortrag: Dr. Lars Kindler (FU Berlin)

Vortrag: Dr. Victoria Hoskins (FU Berlin)

Vortrag: Dr. Joana Cirici (FU Berlin)

Mathe. Kolloquium: Prof. Ian Hambleton (McMaster)

Mathe. Kolloquium: PD Dr. Daniela Kraus (Würzburg)

Mathe. Kolloquium: Prof. Boris Hasselblatt (Tufts University, Medford, MA/US)

Mathe. Kolloquium: Harald Helfgott (CNRS - Paris)

Mathe. Kolloquium: Dr. Vijaya Trivedi (Mumbai / Berlin)