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 Mosc. Math. J., 2018, Volume 18, Number 2, Pages 193–204 (Mi mmj670)

On the characteristic foliation on a smooth hypersurface in a holomorphic symplectic fourfold

E. Amerikab, L. Gusevaa

a National Research University Higher School of Economics, Laboratory of Algebraic Geometry and Applications, Usacheva 6, 119048 Moscow, Russia
b Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, Campus Scientifique d'Orsay, Bât. 307, 91405 Orsay, France

Abstract: Let $X$ be an irreducible holomorphic symplectic fourfold and $D$ a smooth hypersurface in $X$. It follows from a result by E. Amerik and F. Campana that the characteristic foliation (that is the foliation given by the kernel of the restriction of the symplectic form to $D$) is not algebraic unless $D$ is uniruled. Suppose now that the Zariski closure of its general leaf is a surface. We prove that $X$ has a lagrangian fibration and $D$ is the inverse image of a curve on its base.

Key words and phrases: holomorphic symplectic manifolds, foliations, elliptic surfaces.

Full text: http://www.mathjournals.org/.../2018-018-002-001.html
References: PDF file   HTML file

Document Type: Article
MSC: 14D06, 14D15, 37F75
Language: English

Citation: E. Amerik, L. Guseva, “On the characteristic foliation on a smooth hypersurface in a holomorphic symplectic fourfold”, Mosc. Math. J., 18:2 (2018), 193–204

Citation in format AMSBIB
\Bibitem{AmeGus18} \by E.~Amerik, L.~Guseva \paper On the characteristic foliation on a~smooth hypersurface in a~holomorphic symplectic fourfold \jour Mosc. Math.~J. \yr 2018 \vol 18 \issue 2 \pages 193--204 \mathnet{http://mi.mathnet.ru/mmj670}