论文标题
$ \ mathbb {q} $的hodge理想的消失 - 除数
Vanishing for Hodge ideals of $\mathbb{Q}$-divisors
论文作者
论文摘要
MustaţăA和Popa介绍了有效的$ \ Mathbb {q} $ - Divisor $ d $的霍奇理想概念，并证明了霍奇理想的消失定理，该定理概括了纳德尔为乘数理想而消失的纳德尔消失。但是，他们的证明需要额外的假设，即$ \ ell $ - 线束$ \ mathscr {o} _x（\ ell d）$的$ \ ell $ - 根，这对于Nadel消失并不是必需的。在本文中，我们证明，即使没有这个假设，霍奇理想的消失仍然存在。
Mustaţă a and Popa introduce the notion of Hodge ideals for an effective $\mathbb{Q}$-divisor $D$ and prove a vanishing theorem for Hodge ideals, which generalizes Nadel vanishing for multiplier ideals. However, their proof needs an extra assumption on the existence of $\ell$-roots of the line bundle $\mathscr{O}_X(\ell D)$, which is not necessary for Nadel vanishing. In this paper, we prove that vanishing for Hodge ideals still holds even without this assumption.
