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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive
Izv. RAN. Ser. Mat., 2014 Volume 78, Issue 1, Pages 25–36 (Mi im7973)
This article is cited in 4 papers

Lagrangian fibrations on hyperkähler fourfolds

D. Greba, Ch. Lehnb, S. Rollenskec

a Albert Ludwigs University of Freiburg
b Institut Fourier, UFR de Mathématiques
c Bielefeld University, Department of Mathematics

Abstract: In answer to the strong form of a question posed by Beauville, we give a short geometric proof that any hyperkähler fourfold containing a Lagrangian subtorus $L$ admits a holomorphic Lagrangian fibration with fibre $L$.

Keywords: hyperkähler manifold, Lagrangian fibration.

UDC: 514.154

MSC: 53C26, 14D06, 14E30, 32G10, 32G05

Received: 02.03.2012

DOI: 10.4213/im7973


 English version: Izvestiya: Mathematics, 2014, 78:1, 22–33

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© Steklov Math. Inst. of RAS, 2024