Alice Garbagnati
Alice Garbagnati (Università Statale di Milano) посетила Лабораторию в апреле 2018 г. по приглашению научного сотрудника лаборатории К.А. Шрамова.
20 апреля 2018 г. Alice Garbagnati выступила на еженедельном научном семинаре лаборатории с докладом "(Double) Covers of K3 surfaces".
Аннотация: 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.
20 апреля 2018 г. Alice Garbagnati выступила на еженедельном научном семинаре лаборатории с докладом "(Double) Covers of K3 surfaces".
Аннотация: 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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