Related papers: A note on Hessenberg varieties
The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of…
For a connected, simply-connected complex simple algebraic group $G$, we examine a class of Hessenberg varieties associated with the minimal nilpotent orbit. In particular, we compute the Poincar\'{e} polynomials and irreducible components…
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…
In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…
We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…
In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfinitely many times, as these are essential to the proof;…
We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either a non-characteristic vertical plane, or its generalized…
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].
We prove a new theorem of Tverberg type which confirms the conjecture of Blagojevic, Frick, and Ziegler about the existence of "balanced Tverberg partitions" (Conjecture 6.6 in, Tverberg plus constraints, Bull. London Math. Soc., 46 (2014)…
This paper is a contribution to Vinberg's theory of $\theta$-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Springer's theory of regular elements of finite reflection…
In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group…
An technically interesting proof of a known theorem.
This short note proves a generalization of the Hirzebruch Riemann-Roch theorem equivalent to the Cardy condition described in [1]. This is done using an earlier result [4] that explicitly describes what the Mukai pairing in [1] descends to…
We study nonsingular branched coverings of a homogeneous space X. There is a vector bundle associated with such a covering which was conjectured by O. Debarre to be ample when the Picard number of X is one. We prove this conjecture, which…
Let $A_K$ be an abelian variety with semistable reduction over a strictly henselian field of positive characteristic with perfect residue class field. We show that there is a close connection between the pairings of Grothendieck,…
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
We prove that the kernel of the evaluation morphism of global sections - namely the syzygy bundle - of a sufficiently ample line bundle on an abelian variety is stable. This settles a conjecture of Ein-Lazarsfeld-Mustopa, in the case of…