Results 21 to 30 of about 917 (46)

Stable degeneration of families of klt singularities with constant local volume

Forum of Mathematics, Sigma
For a klt singularity, C. Xu and Z. Zhuang [33] proved the associated graded algebra of a minimizing valuation of the normalized volume function is finitely generated, finishing the proof of the stable degeneration conjecture proposed by C. Li and C. Xu.
Zhiyuan Chen
doaj   +1 more source

Complements and coregularity of Fano varieties

Forum of Mathematics, Sigma
We study the relation between the coregularity, the index of log Calabi–Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi–Yau pair $(X,B)$ of coregularity $1$ is at most $120\lambda ^2$ , where
Fernando Figueroa, Stefano Filipazzi, Joaquín Moraga, Junyao Peng   +3 more
doaj   +1 more source

THE ${\it\alpha}$ -INVARIANT AND THOMPSON’S CONJECTURE

Forum of Mathematics, Pi, 2016
In 1981, Thompson proved that, if $n\geqslant 1$ is any integer and $G$
PHAM HUU TIEP
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The complex gradient inequality with parameter [PDF]

, 2014
We prove that given a holomorphic family of holomorphic functions with isolated singularities at zero and constant Milnor number, it is possible to obtain the gradient inequality with a uniform exponent.Comment: A remark was added at the end and some ...
Denkowski, Maciej P.
core  

Coordinate rings of regular nilpotent Hessenberg varieties in the open opposite schubert cell

Forum of Mathematics, Sigma
Dale Peterson has discovered a surprising result that the quantum cohomology ring of the flag variety $\operatorname {\mathrm {GL}}_n({\mathbb {C}})/B$ is isomorphic to the coordinate ring of the intersection of the Peterson variety ...
Tatsuya Horiguchi, Tomoaki Shirato
doaj   +1 more source

Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms

, 2016
We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in $\mathbb{C}^3$ is a bi-Lipschitz invariant.Comment ...
Fernandes, Alexandre, Sampaio, J. Edson
core   +1 more source

On the embedded Nash problem

Forum of Mathematics, Pi
The embedded Nash problem for a hypersurface in a smooth algebraic variety is to characterize geometrically the maximal irreducible families of arcs with fixed order of contact along the hypersurface.
Nero Budur, Javier de la Bodega, Eduardo de Lorenzo Poza, Javier Fernández de Bobadilla, Tomasz Pełka   +4 more
doaj   +1 more source

Stable tangential families and singularities of their envelopes [PDF]

, 2004
We study tangential families, i.e. systems of rays emanating tangentially from given curves. We classify, up to Left-Right equivalence, stable singularities of tangential family germs (under deformations among tangential families) and we study their ...
Capitanio, Gianmarco
core   +2 more sources

Strict positivity of Kähler–Einstein currents

Forum of Mathematics, Sigma
Kähler–Einstein currents, also known as singular Kähler–Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular compact Kähler spaces X and their two defining properties are the following:
Vincent Guedj, Henri Guenancia, Ahmed Zeriahi   +2 more
doaj   +1 more source

Legendrian graphs generated by Tangential Families [PDF]

, 2004
We construct a Legendrian version of Envelope theory. A tangential family is a 1-parameter family of rays emanating tangentially from a smooth plane curve.
Capitanio, Gianmarco
core   +2 more sources