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摘要翻译：
设$X\子集\MathBB P^{n+1}$是光滑复射影超曲面。本文证明了如果$x$的阶足够大，则在$x$上存在$n$级不变喷射微分丛的全局截面，且在一个充分的除数上消失。我们还证明了对数对$(\mathbb p^n,D)$的低维有效的对数形式，其中$D$是高阶光滑不可约因子。而且，这些结果是尖锐的，\emph{即}一个人不能有这样的级数小于$N$的喷射微分。
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英文标题：
《Existence of global invariant jet differentials on projective
hypersurfaces of high degree》
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作者：
Simone Diverio
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最新提交年份：
2008
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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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一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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英文摘要：
Let $X\subset\mathbb P^{n+1}$ be a smooth complex projective hypersurface. In this paper we show that, if the degree of $X$ is large enough, then there exist global sections of the bundle of invariant jet differentials of order $n$ on $X$, vanishing on an ample divisor. We also prove a logarithmic version, effective in low dimension, for the log-pair $(\mathbb P^n,D)$, where $D$ is a smooth irreducible divisor of high degree. Moreover, these result are sharp, \emph{i.e.} one cannot have such jet differentials of order less than $n$.
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PDF链接：
https://arxiv.org/pdf/0802.0045
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