Deformation theory of singular symplectic n-folds
Deformation theory of singular symplectic n-folds
复制标题
奇异辛n重变形理论
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Y. Namikawa
中科院分区：
文献类型：
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作者：
Y. Namikawa
辛流形（或辛n褶）是指偶数维n的紧化Kaehler流形，具有非简并全纯的2型ω，即ω是一个不灭的n型。这个概念可以推广到有奇点的变种。如果X是具有有理Gorenstein奇点的正规射影变，且X的正则轨迹U允许非简并全纯2型ω，则称X为射影辛变。在广义Bogomolov分解猜想中，辛变种与奇异Calabi-Yau变种一起起着重要的作用。现在基本上已经发现了几个辛流形的例子，通过变形辛流形来寻找新的辛流形似乎是一项重要的任务。本文从变形理论的角度研究了一种射影辛变分。如果X具有分辨率π: X→X，使得（X, πω）是辛流形，我们说X具有辛分辨率。我们的第一个结果是关于辛流形的两族收缩映射。
By a symplectic manifold (or a symplectic n-fold) we mean a compact Kaehler manifold of even dimension n with a non-degenerate holomorphic 2form ω, i.e. ω is a nowhere-vanishing n-form. This notion is generalized to a variety with singularities. We call X a projective symplectic variety if X is a normal projective variety with rational Gorenstein singularities and if the regular locus U of X admits a non-degenerate holomorphic 2-form ω. A symplectic variety will play an important role together with a singular Calabi-Yau variety in the generalized Bogomolov decomposition conjecture. Now that essentially a few examples of symplectic manifolds are discovered, it seems an important task to seek new symplectic manifolds by deforming symplectic varieties. In this paper we shall study a projective symplectic variety from a view point of deformation theory. If X has a resolution π : X → X such that (X, πω) is a symplectic manifold, we say that X has a symplectic resolution. Our first results are concerned with a birational contraction map of a symplectic manifold.