EPW-sextics are special 4-dimensional sextic hypersurfaces (with 20 moduli) which come equipped with a double cover. We analyze the double cover of EPW-sextics parametrized by a certain prime divisor in the moduli space. We associate to the generic sextic parametrized by that divisor a K3 surface of genus 6 and we show that the double epw sextic is a contraction of the Hilbert square of the K3. This result has two consequences. First it gives a new proof of the following result of ours: smooth double EPW-sextics form a locally complete family of hyperkaehler projective deformations of the Hilbert square of a K3. Secondly it shows that away from another prime divisor in the moduli space the period map for double EPW-sextics is as well-behaved as it possibly could be.
Double covers of EPW-sextics / O'Grady, Kieran Gregory. - In: MICHIGAN MATHEMATICAL JOURNAL. - ISSN 0026-2285. - STAMPA. - 62:1(2013), pp. 143-184. [10.1307/mmj/1363958245]
Double covers of EPW-sextics
O'GRADY, Kieran Gregory
2013
Abstract
EPW-sextics are special 4-dimensional sextic hypersurfaces (with 20 moduli) which come equipped with a double cover. We analyze the double cover of EPW-sextics parametrized by a certain prime divisor in the moduli space. We associate to the generic sextic parametrized by that divisor a K3 surface of genus 6 and we show that the double epw sextic is a contraction of the Hilbert square of the K3. This result has two consequences. First it gives a new proof of the following result of ours: smooth double EPW-sextics form a locally complete family of hyperkaehler projective deformations of the Hilbert square of a K3. Secondly it shows that away from another prime divisor in the moduli space the period map for double EPW-sextics is as well-behaved as it possibly could be.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.