Quot schemes and moduli spaces

Diplôme Thèse Quot schemes and moduli spaces eng 2016-06-06 author Juhasz Mate 699133 director Szenes Andras 664272 10.13097/archive-ouverte/unige:85000 urn:nbn:ch:unige-850009 Sc. 4934 Consider the moduli space M of stable vector bundles over a curve. Verlinde's formulas give the cohomologies of line bundles over M. We develop a novel method to recalculate this. Consider two birationally equivalent spaces, a Quot scheme Q and a projective fibration P, with a PGL(n) action. By lifting the PGL(n) action on P to a line bundle L, the GIT quotient is a fibration over M with an induced line bundle L'. By the [Q,R]=0 theorem, the cohomologies of L' correspond to the invariant part of the cohomologies of L. The Atiyah-Bott localization formula gives the equivariant Euler characteristic of L. The main idea is to apply this formula to Q instead of P. The main conjecture is that we get the same results as using P. We calculate the formula for certain parameters and verify the conjecture for those cases. Quot scheme Moduli space Stable vector bundle Verlinde's formula Geometric invariant theory Atiyah-Bott localization Dewey 510 25 Section de mathématiques 11 false 6239a683-4554-41ce-93f2-e128f5fa1ad5 Thesis Public diss045h-1-A.pdf 1200333 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Juhasz, Mate