Varieties with rational singularities

1987 ◽  
pp. 179-182
Author(s):  
George R. Kempf
Keyword(s):  
Rational Singularities

scholarly journals Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities

2017 ◽  
Vol 291 (2-3) ◽  
pp. 245-263 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Multiplier Ideals ◽  
Rational Singularities

scholarly journals Existence and Density of General Components of the Noether–Lefschetz Locus on Normal Threefolds

2020 ◽  
Author(s):  
Ugo Bruzzo ◽  
Antonella Grassi ◽  
Angelo Felice Lopez
Keyword(s):  
Natural Topology ◽  
Rational Singularities

Abstract We consider the Noether–Lefschetz problem for surfaces in ${\mathbb Q}$-factorial normal 3-folds with rational singularities. We show the existence of components of the Noether–Lefschetz locus of maximal codimension, and that there are indeed infinitely many of them. Moreover, we show that their union is dense in the natural topology.

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 PROJECTIVITY CRITERION OF MOISHEZON SPACES AND DENSITY OF PROJECTIVE SYMPLECTIC VARIETIES

2002 ◽  
Vol 13 (02) ◽  
pp. 125-135 ◽  
Author(s):  
YOSHINORI NAMIKAWA
Keyword(s):  
Kähler Manifold ◽  
Projective Manifold ◽  
Singular Case ◽  
Isolated Singularities ◽  
Rational Singularities ◽  
Kahler Manifold ◽  
Moishezon Space ◽  
Symplectic Varieties

A Moishezon manifold is a projective manifold if and only if it is a Kähler manifold [13]. However, a singular Moishezon space is not generally projective even if it is a Kähler space [14]. Vuono [19] has given a projectivity criterion for Moishezon spaces with isolated singularities. In this paper we shall prove that a Moishezon space with 1-rational singularities is projective when it is a Kähler space (Theorem 1.6). We shall use Theorem 1.6 to show the density of projective symplectic varieties in the Kuranishi family of a (singular) symplectic variety (Theorem 2.4), which is a generalization of the result by Fujiki [4, Theorem 4.8] to the singular case. In the Appendix we give a supplement and a correction to the previous paper [15] where singular symplectic varieties are dealt with.

scholarly journals Hankel determinantal rings have rational singularities

2018 ◽  
Vol 335 ◽  
pp. 111-129 ◽  
Author(s):  
Aldo Conca ◽  
Maral Mostafazadehfard ◽  
Anurag K. Singh ◽  
Matteo Varbaro
Keyword(s):  
Rational Singularities

scholarly journals A modular compactification of ℳ1,n from A∞-structures

2019 ◽  
Vol 2019 (755) ◽  
pp. 151-189
Author(s):  
Yankı Lekili ◽  
Alexander Polishchuk
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Rational Singularities ◽  
Picard Groups

AbstractWe show that a certain moduli space of minimal A_{\infty}-structures coincides with the modular compactification {\overline{\mathcal{M}}}_{1,n}(n-1) of \mathcal{M}_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n\leq 11.

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