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Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds
We generalize the classical approach of describing the infinitesimal Torelli map in terms of multiplication in a Jacobi ring to the case of...
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Categorical Torelli theorems: results and open problems
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective...
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Teichmüller spaces and Torelli theorems for hyperkähler manifolds
Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract...
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A refined derived Torelli theorem for Enriques surfaces
We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from 2 are isomorphic if their...
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Bergman kernel and period map for curves
As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra....
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Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds
Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ⊂ Ω. In terms of the...
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Hyper-Kähler Manifolds
The aim of this introductory survey is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their...
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On the dimension of totally geodesic submanifolds in the Prym loci
In this paper we give a bound on the dimension of a totally geodesic submanifold of the moduli space of polarised abelian varieties of a given...
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Action of the Automorphism Group on the Jacobian of Klein’s Quartic Curve
Klein’s simple group H of order 168 is the automorphism group of the plane quartic curve C4, called Klein quartic. By Torelli Theorem, the full...
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