Related papers: The structure of algebraic varieties
We discuss the role played by logarithmic structures in the theory of moduli.
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions. The results are applied to study the isogeny decomposition of Weil restrictions.
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
These are notes for a series of five lectures on "Moduli and degenerations of algebraic curves via tropical geometry" delivered at the CIMPA-CIMAT-ICTP School on Moduli of Curves, February 29-March 4, 2016 in Guanajuato, Mexico.
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
We survey on algebraically elliptic varieties in the sense of Gromov.
These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…
We construct the fine moduli space of log abelian varieties with PEL structure, which gives a toroidal compactification of the moduli space of abelian varieties with PEL structure.
For the affine Lie algebra $C_2^{(1)}$ we study non-principal and non-coprincipal admissible modules of integer level and their quantum Hamiltonian reduction, and show that they have $\Gamma_0(2)$-modular invariance.
These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.
This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…
We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…
Arithmetic quotients are quotients of bounded symmetric domains by arithmetic groups, and modular subvarieties of arithmetic quotients are themselves arithmetic quotients of lower dimension which live on arithmetic quotients, by an…
Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…
We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…
The purpose of this paper is to describe explicitly the modules of (Siegel-)Jacobi forms of degree two of index one of any scalar valued weight with respect to some congruence subgroups of small levels $N\leq 4$. Such a structure for the…