scholarly journals Hodge filtration, minimal exponent, and local vanishing

2019 ◽  
Vol 220 (2) ◽  
pp. 453-478 ◽  
Author(s):  
Mircea Mustaţă ◽  
Mihnea Popa
Keyword(s):  
Hodge Filtration

scholarly journals Twisted Hodge filtration: Curvature of the determinant

2019 ◽  
Vol 292 (11) ◽  
pp. 2452-2455
Author(s):  
Philipp Naumann
Keyword(s):  
Hodge Filtration

scholarly journals LOCAL VANISHING AND HODGE FILTRATION FOR RATIONAL SINGULARITIES

2018 ◽  
Vol 19 (3) ◽  
pp. 801-819
Author(s):  
Mircea Mustaţă ◽  
Sebastián Olano ◽  
Mihnea Popa
Keyword(s):  
Toric Variety ◽  
Exceptional Divisor ◽  
Resolution Of Singularities ◽  
Isolated Singularities ◽  
Rational Singularities ◽  
Smooth Complex ◽  
Hodge Filtration ◽  
Generation Level ◽  
Image Position

Given an $n$-dimensional variety $Z$ with rational singularities, we conjecture that if $f:Y\rightarrow Z$ is a resolution of singularities whose reduced exceptional divisor $E$ has simple normal crossings, then $$\begin{eqnarray}\displaystyle R^{n-1}f_{\ast }\unicode[STIX]{x1D6FA}_{Y}(\log E)=0. & & \displaystyle \nonumber\end{eqnarray}$$ We prove this when $Z$ has isolated singularities and when it is a toric variety. We deduce that for a divisor $D$ with isolated rational singularities on a smooth complex $n$-dimensional variety $X$, the generation level of Saito’s Hodge filtration on the localization $\mathscr{O}_{X}(\ast D)$ is at most $n-3$.

scholarly journals Nilpotence of Frobenius action and the Hodge filtration on local cohomology

2017 ◽  
Vol 305 ◽  
pp. 456-478 ◽  
Author(s):  
Vasudevan Srinivas ◽  
Shunsuke Takagi
Keyword(s):  
Local Cohomology ◽  
Hodge Filtration

scholarly journals On Plane Curves with Double and Triple Points

2016 ◽  
Vol 119 (1) ◽  
pp. 60 ◽  
Author(s):  
Nancy Abdallah
Keyword(s):  
Plane Curve ◽  
Plane Curves ◽  
Jacobian Ideal ◽  
Pole Order ◽  
Hodge Filtration ◽  
Triple Points

We describe in simple geometric terms the Hodge filtration on the cohomology $H^*(U)$ of the complement $U=\mathsf{P}^2 \setminus C$ of a plane curve $C$ with ordinary double and triple points. Relations to Milnor algebra, syzygies of the Jacobian ideal and pole order filtration on $H^2(U)$ are given.

scholarly journals IRREGULAR HODGE FILTRATION OF SOME CONFLUENT HYPERGEOMETRIC SYSTEMS

2019 ◽  
pp. 1-42 ◽  
Author(s):  
Alberto Castaño Domínguez ◽  
Christian Sevenheck
Keyword(s):  
Laurent Polynomials ◽  
Hodge Filtration ◽  
Comparison Results ◽  
Hodge Numbers

We determine the irregular Hodge filtration, as introduced by Sabbah, for the purely irregular hypergeometric${\mathcal{D}}$-modules. We obtain, in particular, a formula for the irregular Hodge numbers of these systems. We use the reduction of hypergeometric systems from GKZ-systems as well as comparison results to Gauss–Manin systems of Laurent polynomials via Fourier–Laplace and Radon transformations.

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