对数辛流形的复形、残数和阻挡

Pub Date : 2022-11-07 DOI:10.1007/s10455-022-09881-x

Ziv Ran

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引用次数: 0

摘要

我们考虑偶数维4或更大的紧致Kählerian流形X，它被赋予一个对数辛结构\（\Phi\），一个在除数D上具有单极点的一般非退化闭2-形式，具有局部正交。一个简单的线性不等式涉及\（\Phi\）在D的双轨迹分量上的迭代庞加莱残基，它确保了对\（（X，\Phi）\）具有无阻碍的变形，并且D局部平凡地变形。

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Complexes, residues and obstructions for log-symplectic manifolds

We consider compact Kählerian manifolds X of even dimension 4 or more, endowed with a log-symplectic structure \(\Phi \), a generically nondegenerate closed 2-form with simple poles on a divisor D with local normal crossings. A simple linear inequality involving the iterated Poincaré residues of \(\Phi \) at components of the double locus of D ensures that the pair \((X, \Phi )\) has unobstructed deformations and that D deforms locally trivially.

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