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# Conference - Teichmüller Theory in Higher Dimension and Mirror Symmetry

Thursday, April 27, 2017 - 15:15
Fabrizio Catanese
Bayreuth
Teichmueller space and automorphisms
Abstract:

The most well known case of Teichmueller space is the one of complex tori, which yield a connected component of $\mathcal{T}(T)$ isomorphic to an open set of a Grassmannian. I shall present some recent results, the first joint with Pietro Corvaja, on the Teichmueller space of Generalized Hyperelliptic manifolds. These are finite free quotients $X = T/G$ of a complex torus. Using an algebraic result which says that a cristallographic group has a unique natural affine representation, we can describe natural components for $\mathcal{T}(X)$, again open sets in suitable Grassmannian. I shall then describe some joitn work with Gromadski , on surfaces of general type with automorphisms acting trivially on cohomology, respectively trivially on rational but not on integral cohomology. For irregular surfaces conjecturally there are no nontrivial automorphisms isotopic to the identity.