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The Hodge diamond of O’Grady’s six-dimensional example

Part of: Birational geometry (Co)homology theory Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  21 March 2018

Giovanni Mongardi ,
Antonio Rapagnetta  and
Giulia Saccà
Giovanni Mongardi
Affiliation:
Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna, Piazza di Porta San Donato 5, Bologna 40126, Italia email giovanni.mongardi2@unibo.it
Antonio Rapagnetta
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma 00133, Italia email rapagnet@axp.mat.uniroma2.it
Giulia Saccà
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11974-3651, USA email giulia.sacca@stonybrook.edu
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Abstract

We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of $\text{K3}^{[3]}$ type by a birational involution, thereby computing its Hodge numbers.

Keywords

irreducible holomorphic symplectic manifoldsHodge numbersO’Grady’s six-dimensional manifold

MSC classification

Primary: 14J40: $n$-folds ($n>4$)
Secondary: 14E07: Birational automorphisms, Cremona group and generalizations 14F05: Sheaves, derived categories of sheaves and related constructions

Information

Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 5 , May 2018 , pp. 984 - 1013
Copyright
© The Authors 2018 

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