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摘要翻译：
我们研究了复射影流形X,它允许至少二次满射自同态f:x->X。在f为etale的情况下，我们证明了描述X的结构定理。特别地，当X是一个未变的三重结构时，我们给出了一个比较详细的描述。对于分枝情形，我们首先证明了射影流形的Galois覆盖的向量丛在很温和的条件下是充足的。这应用于第二Betti数为1的Fano流形的分支自同态的研究。推测射影空间是唯一允许D>1次自同态的Fano流形，并在几种情况下证明了这一点。部分论证是基于射影空间的一个新的刻画，射影空间是唯一的流形，它的切丛中有一个充足的子束。
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英文标题：
《Endomorphisms of projective varieties》
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作者：
Marian Aprodu, Stefan Kebekus and Thomas Peternell
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We study complex projective manifolds X that admit surjective endomorphisms f:X->X of degree at least two. In case f is etale, we prove structure theorems that describe X. In particular, a rather detailed description is given if X is a uniruled threefold. As to the ramified case, we first prove a general theorem stating that the vector bundle associated to a Galois covering of projective manifolds is ample (resp. nef) under very mild conditions. This is applied to the study of ramified endomorphisms of Fano manifolds with second Betti number one. It is conjectured that the projective space is the only Fano manifold admitting admitting an endomorphism of degree d>1, and we prove that in several cases. A part of the argumentation is based on a new characterization of the projective space as the only manifold that admits an ample subsheaf in its tangent bundle.
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PDF链接：
https://arxiv.org/pdf/0705.4602
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