Doctoral thesis
Open access

Quot schemes and moduli spaces

ContributorsJuhasz, Mate
Defense date2016-06-06

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
Citation (ISO format)
JUHASZ, Mate. Quot schemes and moduli spaces. 2016. doi: 10.13097/archive-ouverte/unige:85000
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Creation06/27/2016 11:27:00 AM
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