Author
Taro Fujisawa
Bio: Taro Fujisawa is an academic researcher from Tokyo Denki University. The author has contributed to research in topics: Hodge theory & Hodge structure. The author has an hindex of 10, co-authored 21 publications receiving 256 citations.
Papers
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TL;DR: In this article, the authors discuss the variations of mixed Hodge structure for cohomology with compact support of simple normal crossing pairs and prove a generalization of the Fujita-Kawamata semi-positivity theorem.
Abstract: We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove a generalization of the Fujita–Kawamata semi-positivity theorem.
56 citations
TL;DR: In this article, it was shown that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the dualising sheaves.
Abstract: We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the dualizing sheaves of smooth varieties. Using the weight spectral sequence of mixed Hodge modules, we then reduce the semipositivity theorem for the higher direct images of dualizing sheaves to the smooth case where the assertion is well known. This may be used to simplify some constructions in a recent paper of Y. Kawamata. We also give a simple proof of the semipositivity theorem for admissible variations of mixed Hodge structure in [FF] by using the theories of Cattani, Kaplan, Schmid, Steenbrink, and Zucker. This generalizes Kawamata’s classical result in the pure case. 2010 Mathematics Subject Classification: Primary 14D07; Secondary 32G20.
44 citations
Posted Content•
TL;DR: In this article, a generalization of the Fujita-Kawamata semi-positivity theorem for mixed Hodge structures with compact support of simple normal crossing pairs is presented.
Abstract: We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove a generalization of the Fujita--Kawamata semi-positivity theorem.
40 citations
Posted Content•
TL;DR: In this article, it was shown that the moduli part of a basic slc-trivial fibration is semiample when the base space is a curve and that it is b-numerically trivial.
Abstract: We prove that if the moduli $\mathbb Q$-b-divisor of a basic slc-trivial fibration is b-numerically trivial then it is $\mathbb Q$-b-linearly trivial. As a consequence, we prove that the moduli part of a basic slc-trivial fibration is semi-ample when the base space is a curve.
23 citations
Journal Article•
TL;DR: In this paper, the relationship of constructions of cohomological mixed Hodge complexes and related l-adic constructions by various authors systemically is studied. But the relationship is not discussed.
Abstract: We study the relationship of constructions of cohomological mixed Hodge complexes and related l-adic constructions by various authors system- atically.
19 citations
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TL;DR: Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described in this article with a basic knowledge of cohology theory, the background necessary to understand Hodge theory and polarization.
Abstract: With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.
229 citations
01 Mar 2014
TL;DR: In this paper, it was shown that every quasi-projective semi-log canonical pair has a natural quasi-log structure with several good properties, including vanishing theorems, torsion-free theorem, and the cone and contraction theorem.
Abstract: We prove that every quasi-projective semi log canonical pair has a natural quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log canonical pairs.
100 citations
Journal Article•
TL;DR: In this article, the logarithmic version of the Riemann- Hilbert correspondence defined in (KtNk) was generalized to local systems with quasi-unipotent local monodromies by working with a certain Grothendieck topology.
Abstract: We generalize the logarithmic version of the Riemann- Hilbert correspondence defined in (KtNk) to local systems with quasi- unipotent local monodromies by working with a certain Grothendieck topology. We also discuss its behavior with respect to direct images and give applications to nearby cycles and the degeneration of relative log Hodge to log de Rham spectral sequences.
72 citations
TL;DR: In this article, the authors discuss the variations of mixed Hodge structure for cohomology with compact support of simple normal crossing pairs and prove a generalization of the Fujita-Kawamata semi-positivity theorem.
Abstract: We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove a generalization of the Fujita–Kawamata semi-positivity theorem.
56 citations
TL;DR: In this article, a smooth projective morphism between smooth complex projective varieties is considered and it is shown that if the source space is a weak Fano (or Fano) manifold, then so is the target space.
Abstract: We consider a smooth projective morphism between smooth complex projective varieties. If the source space is a weak Fano (or Fano) manifold, then so is the target space. Our proof is Hodge theoretic. We do not need mod p reduction arguments. We also discuss related topics and questions.
55 citations