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A study of compact complex manifolds admitting non-isomorphic surjective endomorphisms

承认非同构满射自同态的紧复流形的研究

基本信息

批准号：
23540055
负责人：
FUJIMOTO Yoshio
金额：
$ 1.91万
依托单位：
Nara Medical University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2011
资助国家：
日本
起止时间：
2011 至 2013
项目状态：
已结题

项目摘要

We have studied structures of smooth projective 3-folds X with negative Kodaira dimension admitting non-isomorphic \'{e}tale endomorphisms. We can show that a suitable finite \'{e}tale covering X' of X is classified into 6 types. There exists some X where X' cannot be decomposed as a product of a uniruled surface and an elliptic curve. The contraction morphism associated to R is the inverse of a blow-up of another smooth 3-fold along an elliptic curve. The trouble is that R cannot necessarily be stabilized by a suitable power of f. Hence the minimal model program(MMP) cannot work so as to be compatible with endomorphisms. As a substitute, we consider the tower of non-isomorphic finite \'{e}tale covering of 3-folds (called ESP), on which MMP works well. Such a 3-fold X can be obtained as a succession of blow-ups along an elliptic curve from a characteristic ESP (called DESP). We can also give a simple criterion for certan conic bundles to have non-isomorphic \'{e}tale endomorphisms.

研究了具有负科代拉维数且允许非同构自同态的光滑射影3-折叠X的结构.我们可以证明，X的一个合适的覆盖X'的有限尾可分为6种类型.存在某个X，其中X'不能分解为一个非圆曲面和一条椭圆曲线的乘积。与R相关联的收缩态射是另一条光滑3重沿着椭圆曲线的爆破的逆。问题是R不一定能被f的适当幂稳定。因此，最小模型程序（MMP）不能与自同态相容。作为替代，我们考虑了3-folds的非同构有限故事覆盖的塔（称为ESP），MMP在其上工作得很好。这样一个3重X可以通过一个特征ESP（称为DESP）沿一条椭圆曲线沿着的一系列爆破来获得。我们还可以给出某些锥丛具有非同构的自同态的一个简单判据。