2018
DOI: 10.48550/arxiv.1810.11011
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Lagrangian fibrations for IHS fourfolds

Abstract: In this paper we study the Lagrangian fibrations for projective irreducible symplectic fourfolds and exclude the case of non-smooth base. Our method could be extended to the higherdimensional cases.

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Cited by 6 publications
(11 citation statements)
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“…Singularities of the base. It is generally expected that the base manifold B is smooth, but at the moment this is only known for n ď 2, see [Ou19,BK18,HX19]. The expectation is corroborated by the following computations of invariants of the singularities of B.…”
Section: Basics On Lagrangian Fibrationsmentioning
confidence: 74%
“…Singularities of the base. It is generally expected that the base manifold B is smooth, but at the moment this is only known for n ď 2, see [Ou19,BK18,HX19]. The expectation is corroborated by the following computations of invariants of the singularities of B.…”
Section: Basics On Lagrangian Fibrationsmentioning
confidence: 74%
“…2 By [36, Theorem 3 (3)], a general fiber of a Lagrangian fibration associated with any irreducible symplectic variety is an abelian variety. 3 The fact that Matsushita's example is irreducible symplectic is verified by [34,Proposition 2.5].…”
Section: Introductionmentioning
confidence: 96%
“…This was confirmed by Hwang [23] assuming B nonsingular, and remained wide open in general. See also [33,22,3] for recent progress.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…1 For background on Lagrangian fibrations, cf. the foundational [29] as well as the recent [7], [18] and the references given there.…”
Section: Introductionmentioning
confidence: 96%