2021/04/11 by Junchao Shentu, Chen Zhao, Shentu, Junchao +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2104.04905
In this paper, we introduce a coherent subsheaf of Saito's S-sheaf, which is a combination of the S-sheaf and the multiplier ideal sheaf. We construct its L2-Dolbeault resolution, which generalizes MacPherson's conjecture on the L2 resolution of the Grauert-Riemenschneider sheaf. We also prove various vanishing theorems for the S-sheaf (Saito's vanishing theorem, Kawamata-Viehweg vanishing theorem and some new ones like Nadel vanishing theorem) transcendentally. Finally, we discuss some applications of our results on the relative version of Fujita's conjecture (e.g. Kawamata's conjecture).