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pro vyhledávání: '"Shen, Wanchun"'
We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides some extensio
Externí odkaz:
http://arxiv.org/abs/2409.18019
Autor:
Popa, Mihnea, Shen, Wanchun
We compute the Du Bois complexes of abstract cones over singular varieties, and use this to describe the local cohomological dimension and the non-positive K-groups of such cones.
Comment: 18 pages; for a volume in memory of Lucian Badescu
Comment: 18 pages; for a volume in memory of Lucian Badescu
Externí odkaz:
http://arxiv.org/abs/2406.03593
Let $X$ be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves $R^if_*\Omega^p_{\tilde X}(\log E)$, where $f: \tilde{X} \to X$ is a strong log resolution of singularities with reduced exceptional divisor $E$. These ext
Externí odkaz:
http://arxiv.org/abs/2306.10179
We introduce new notions of $k$-Du Bois and $k$-rational singularities, extending the previous definitions in the case of local complete intersections (lci), to include natural examples outside of this setting. We study the stability of these notions
Externí odkaz:
http://arxiv.org/abs/2306.03977
Autor:
Shen, Wanchun
We introduce a probability distribution on $\mathcal{P}([0,1]^d)$, the space of all Borel probability measures on $[0,1]^d$. Under this distribution, almost all measures are shown to have infinite upper quasi-Assouad dimension and zero lower quasi-As
Externí odkaz:
http://arxiv.org/abs/1909.11132
It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the $3$-fold convolution of the Cantor measure and certain Bernoulli convolutions. In this paper we stu
Externí odkaz:
http://arxiv.org/abs/1909.08941
By a Cantor-like measure we mean the unique self-similar probability measure $\mu $ satisfying $\mu =\sum_{i=0}^{m-1}p_{i}\mu \circ S_{i}^{-1}$ where $% S_{i}(x)=\frac{x}{d}+\frac{i}{d}\cdot \frac{d-1}{m-1}$ for integers $2\leq d
Externí odkaz:
http://arxiv.org/abs/1810.00201
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Publikováno v:
Frontiers in Heat & Mass Transfer; 2024, Vol. 22 Issue 5, p1361-1379, 19p
