Alice Garbagnati
Alice Garbagnati (Università Statale di Milano) visited Laboratory of Algebraic Geometry in April 2019 at the invitation of Research Fellow Konstantin Shramov
On April 20th 2018 Alice Garbagnati gave a talk "(Double) Covers of K3 surfaces" at the seminar of Laboratory.
Abstract:
In the past, the problem to determine finite automorphisms on a K3 surface and their quotients was intensively studied.
If one considers symplectic automorphisms, the quotient admits a desingularization which is still a K3 surface. The main results in this context relate the presence of an automorphism group to certain properties of the Neron-Severi group of the surface, so that one describes the family of K3 surfaces with certain automorphisms as L-polarized families, for certain lattice L.
The converse problem was, quite surprising, less studied: is it possible to describe K3 surfaces which admit certain covers by means of properties of their Neron-Severi groups? In the talk I will report some positive answers to this question, both in the cases where the covering surface is another K3 surface, and in some cases where the cover has order 2 and the covering surface is of general type. In the last part of the talk I restrict attention to double covers which are certain smooth surfaces of general type. The Hodge structure on the second cohomology group of these surfaces naturally contains two different sub-Hodge structures of K3 type. We discuss both of them proving that in certain cases each of them is related to a K3 surface by a geometric constructuion.
On April 20th 2018 Alice Garbagnati gave a talk "(Double) Covers of K3 surfaces" at the seminar of Laboratory.
Abstract:
In the past, the problem to determine finite automorphisms on a K3 surface and their quotients was intensively studied.
If one considers symplectic automorphisms, the quotient admits a desingularization which is still a K3 surface. The main results in this context relate the presence of an automorphism group to certain properties of the Neron-Severi group of the surface, so that one describes the family of K3 surfaces with certain automorphisms as L-polarized families, for certain lattice L.
The converse problem was, quite surprising, less studied: is it possible to describe K3 surfaces which admit certain covers by means of properties of their Neron-Severi groups? In the talk I will report some positive answers to this question, both in the cases where the covering surface is another K3 surface, and in some cases where the cover has order 2 and the covering surface is of general type. In the last part of the talk I restrict attention to double covers which are certain smooth surfaces of general type. The Hodge structure on the second cohomology group of these surfaces naturally contains two different sub-Hodge structures of K3 type. We discuss both of them proving that in certain cases each of them is related to a K3 surface by a geometric constructuion.
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