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
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.
MSC: 14D06, 14D15, 37F75
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
\by E.~Amerik, L.~Guseva
\paper On the characteristic foliation on a~smooth hypersurface in a~holomorphic symplectic fourfold
\jour Mosc. Math.~J.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|