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The Prym-Hitchin connection and strange Prym duality at level 1

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Christian Pauly (Nice) - Seminar Algebraic Geometry (SAG)

What
  • Seminar
When Jun 07, 2018
from 10:30 am to 11:30 am
Where Bonn, Hörsaal MPI, Vivatsgasse 7
Contact Name Sachinidis
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In the first part of this talk I will outline the construction of Hitchin's projective
connection on the sheaf of non-abelian level-l theta functions over the moduli space
of semi-stable rank-r vector bundles over a family of smooth complex projective curves via 
an algebro-geometric approach using heat operators developped by Welters, Hitchin,
van Geemen- de Jong. Then, I will briefly explain why the monodromy representation
of the Hitchin connection has infinite image, except in a small number of cases. This result
stands in contrast with the finiteness of the monodromy of abelian theta functions. I will
concentrate on one of these exceptional cases, namely r=2 and l=4. In that case, Prym
varieties, i.e. anti-invariant loci of Jacobians of curves equipped with an involution, and their
non-abelian analogues, studied by Zelaci, naturally appear in the monodromy problem.
Finally, I will present recent results extending the construction of Hitchin's connection to
families of curves with involutions. This is joint work with Baier, Bolognesi and Martens.