LOCAL VANISHING AND HODGE FILTRATION FOR RATIONAL SINGULARITIES
2018 ◽
Vol 19
(3)
◽
pp. 801-819
Keyword(s):
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 $n-3$.
2002 ◽
Vol 13
(02)
◽
pp. 125-135
◽
2018 ◽
Vol 2020
(21)
◽
pp. 7829-7856
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Keyword(s):
2011 ◽
Vol 11
(2)
◽
pp. 273-287
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1969 ◽
Vol 27
◽
pp. 160-161
1983 ◽
Vol 41
◽
pp. 708-709
1974 ◽
Vol 32
◽
pp. 436-437
1978 ◽
Vol 36
(1)
◽
pp. 548-549
◽