Related papers: On the GIT stratification of prehomogeneous vector…

We say that a group is a $4$-HAT-stabilizer if it is the vertex stabilizer of some connected $4$-valent half-arc-transitive graph. In 2001, Maru\v{s}i\v{c} and Nedela proved that every $4$-HAT-stabilizer must be a concentric group. However,…

We study the prequantization of quasi-presymplectic groupoids and their Hamiltonian spaces using $S^1$-gerbes. We give a geometric description of the integrality condition. As an application, we study the prequantization of the…

We construct the Bruhat-Tits stratification of the reduced basic locus of regular ramified unitary Rapoport-Zink spaces of signature $(n\!-\!1,1)$ at vertex-stabilizer level. To study the Bruhat-Tits strata, we introduce strata…

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…

We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain…

When a reductive group acts on an algebraic variety, a linearized ample line bundle induces a stratification on the variety where the strata are ordered by the degrees of instability. In this paper, we study variation of stratifications…

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we…

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. First we will give a criterion for Ext-vanishing for…

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…

Given a noncommutative Hamiltonian space $A$, we prove that the conjecture ``{\it quantization commutes with reduction}'' holds for $A$. We further construct a semidirect product algebra $A \rtimes \mG^A$, and establish a correspondence…

We classify $R$-spaces that admit a certain natural $\Gamma$-symmetric structure. We further determine the maximal antipodal sets of these structures.

In this paper, we give a Littlewood-Paley characterization for the H\"older-Zygmund spaces $\mathcal{C}^{\sigma}(G)$ ($0< \sigma <\infty$) on a stratified Lie group $G$.

We compute the first, second, third, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques.

For the symmetric group $S_4$ we determine all the integer values taken by its group determinant when the matrix entries are integers.

We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…

In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of…

For the algebra $A$ in the title, its prime, primitive and maximal spectra are classified. The group of automorphisms of $A$ is determined. The simple unfaithful $A$-modules and the simple weight $A$-modules are classified.

Let $X$ be a smooth irreducible projective curve of genus $g$ and gonality 4. We show that the canonical model of $X$ is contained in a uniquely defined surface, ruled by conics, whose geometry is deeply related to that of $X$. This surface…

We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder-Narasimhan (HN) stratification, defined by the instability type of the…