论文标题
渐近消失的定理，用于增厚的共同体
An asymptotic vanishing theorem for the cohomology of thickenings
论文作者
论文摘要
让$ x $成为一个平稳的投影方案$ y $ y $ y $的封闭等等的本地完整交叉点，让$ x_t $表示$ t $ t $ th $ x $在$ y $中的增厚$ x $。修复$ y $上的充分的线条捆绑$ \ Mathcal {O} _y（1）$。我们证明了Kodaira消失的定理的以下渐近表述：存在一个整数$ c $，因此对于所有整数$ t \ geqslant 1 $，共同体学组$ h^k（x_t，x_t，\ nathcal {o} {o} _} _ {x_t} _ {x__t}（j）（j）（j）（j））请注意，对田地的特征或$ x $的单数基因座没有任何限制。我们还构建了示例，说明线性界限确实是最好的，即使在固定尺寸中，常数$ c $也是无限的。
Let $X$ be a closed equidimensional local complete intersection subscheme of a smooth projective scheme $Y$ over a field, and let $X_t$ denote the $t$-th thickening of $X$ in $Y$. Fix an ample line bundle $\mathcal{O}_Y(1)$ on $Y$. We prove the following asymptotic formulation of the Kodaira vanishing theorem: there exists an integer $c$, such that for all integers $t \geqslant 1$, the cohomology group $H^k(X_t,\mathcal{O}_{X_t}(j))$ vanishes for $k < \dim X$ and $j < -ct$. Note that there are no restrictions on the characteristic of the field, or on the singular locus of $X$. We also construct examples illustrating that a linear bound is indeed the best possible, and that the constant $c$ is unbounded, even in a fixed dimension.
