Speaker : Professor Kirti Joshi , University of Arizona Title : “ Vector Bundles on Curves : A Perspective ”
نویسنده
چکیده
Vector bundles on Riemann surfaces (or algebraic curves) play an important role in the theory of Riemann surfaces and appear in many areas of mathematics and also mathematical physics. In this talk we will introduce the audience to some fascinating aspects of this beautiful subject. A large part of the talk is aimed at graduate students familiar with some topology/differential geometry.
منابع مشابه
Moduli of Vector Bundles on Curves in Positive Characteristic
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...
متن کاملAn Explicit Formula for the Generic Number of Dormant Indigenous Bundles
A dormant indigenous bundle is an integrable P-bundle on a proper hyperbolic curve of positive characteristic satisfying certain conditions. Dormant indigenous bundles were introduced and studied in the padic Teichmüller theory developed by S. Mochizuki. Kirti Joshi proposed a conjecture concerning an explicit formula for the degree over the moduli stack of curves of the moduli stack classifyin...
متن کاملModuli of Vector Bundles on Curves in Positive Characteristics
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not ...
متن کاملHitchin-mochizuki Morphism, Opers and Frobenius-destabilized Vector Bundles over Curves
Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. For p sufficiently large (explicitly given in terms of r, g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of degree zero up to isomorphism). This is done by exhibiting a surjective morphism from...
متن کاملOn vector bundles destabilized by Frobenius pull-back
Let X be a smooth projective curve of genus g > 1 over an algebraically closed field of positive characteristic. This paper is a study of a natural stratification, defined by the absolute Frobenius morphism of X, on the moduli space of vector bundles. In characteristic two, there is a complete classification of semi-stable bundles of rank 2 which are destabilized by Frobenius pull-back. We also...
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تاریخ انتشار 2011