D-modules in birational geometry

Abstract

It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical connections are enhanced to sheaf theoretic constructions facilitated by the theory of mixed Hodge modules. The emphasis is placed on the recent theory of Hodge ideals.

21 pages; in the Proceedings of the ICM, Rio de Janeiro, 2018; v2 contains a few corrections and additional results compared to the published version

References in corpus (4)

• An overview of Morihiko Saito's theory of mixed Hodge modules
• Hodge ideals and microlocal V-filtration
• Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms
• Hodge ideals for Q-divisors: birational approach

Cited by in corpus (1)

• Hodge filtration and Hodge ideals for $\mathbb{Q}$-divisors with weighted homogeneous isolated singularities