In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover ilde{Y}_A of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold is birationally equivalent to a moduli space of (twisted) stable sheaves on a K3 surface. In particular, we prove that ilde{Y}_A is birational to the Hilbert scheme of two points on a K3 surface if and only if the Gushel-Mukai fourfold is Hodge-special with discriminant d such that the negative Pell equation P_{d/2}(-1) is solvable in mathbb{Z}.
On the double EPW sextic associated to a Gushel-Mukai fourfold / L. Pertusi. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 100:1(2019 Mar), pp. 83-106. [10.1112/jlms.12205]
On the double EPW sextic associated to a Gushel-Mukai fourfold
L. Pertusi
2019
Abstract
In analogy to the case of cubic fourfolds, we discuss the conditions under which the double cover ilde{Y}_A of the EPW sextic hypersurface associated to a Gushel-Mukai fourfold is birationally equivalent to a moduli space of (twisted) stable sheaves on a K3 surface. In particular, we prove that ilde{Y}_A is birational to the Hilbert scheme of two points on a K3 surface if and only if the Gushel-Mukai fourfold is Hodge-special with discriminant d such that the negative Pell equation P_{d/2}(-1) is solvable in mathbb{Z}.
| File | Dimensione | Formato | |
|---|---|---|---|
|
GM4EPW_v6.pdf
accesso aperto
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
535.43 kB
Formato
Adobe PDF
|
535.43 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
