论文标题
一般两极分化的阿伯利亚品种的投射正态性和基础宽敞阈值
Projective normality and basepoint-freeness thresholds of general polarized abelian varieties
论文作者
论文摘要
对于极化的Abelian品种$（X，L）$，Z。Jiang和G. Pareschi引入了一个不变的$β（x，l）$，称为BasePoint-Forpoint-Forpoint-Forpoint-Forpoint-Forpoint-Formoints Threshold。使用这种不变，我们表明，如果$χ（l）\ geq 2^{2G-1} $，尺寸$ g $的一般两极化的Abelian品种$（x，l）$是正常的，而$ L $的类型不是$（2,4，\ dots，4）$。该界限很敏锐，因为众所周知，任何两极分化的Abelian类型$ $（2,4，\ dots，4）$不正常。我们还将$β（x，l）$应用于$ y \ in | l | $的Infititesimal Torelli定理。
For a polarized abelian variety $(X,L)$, Z. Jiang and G. Pareschi introduce an invariant $β(X,L)$, called the basepoint-freeness threshold. Using this invariant, we show that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $χ(L) \geq 2^{2g-1}$ and the type of $L$ is not $(2,4,\dots,4)$. This bound is sharp since it is known that any polarized abelian variety of type $(2,4,\dots,4)$ is not projectively normal. We also give an application of $β(X,L)$ to the Infinitesimal Torelli Theorem for $Y \in |L|$.
