Torus fibers and the weight filtration

2019/08/14 by Andrew Harder, Harder, Andrew
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1908.05110

openalex publication_date 2019/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if (X,Y) is a simple normal crossings log Calabi--Yau pair, then there is a real torus of dimension equal to the codimension of the smallest stratum of Y which can be used to construct W_2k-1H^k(X ∖ Y;ℚ) for all k. We show that an analogous result holds for degenerations of Calabi--Yau varieties. We use this to show that P=W type results hold for pairs (X,Y) consisting of a rational surface X and a nodal anticanonical divisor Y, and for K3 surfaces.

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