Related papers: Stringy E-functions of varieties with A-D-E singul…

We propose a conjectural framework for computing Gorenstein measures and stringy Hodge numbers in terms of motivic integration over arcs of smooth Artin stacks, and we verify this framework in the case of fantastacks, which are certain…

We continue study of some algebraic varieties (called resultantal varieties) started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions of Carlitz modules". These varieties are related with the…

We calculate the E-polynomial for a class of the (complex) character varieties $\mathcal{M}_n^{\tau}$ associated to a genus $g$ Riemann surface $\Sigma$ equipped with an orientation reversing involution $\tau$. Our formula expresses the…

Let $k$ be an algebraically closed field of positive characteristic. For any integer $m \geq 2$, we show that the Hodge numbers of a smooth projective $k$-variety can take on any combination of values modulo $m$, subject only to Serre…

In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Hacon, and Mihai P\u{a}un.

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…

We investigate the relations between the rings ${\bf E}$, ${\bf G}$ and ${\bf D}$ of values taken at algebraic points by arithmetic Gevrey series of order either $-1$ ($E$-functions), $0$ (analytic continuations of $G$-functions) or $1$…

Let $G$ be a complex reductive group, $\theta \colon G \to G$ an involution, and $K = G^\theta$. In arXiv:1206.5547, W. Schmid and the second named author proposed a program to study unitary representations of the corresponding real form…

We recall the construction of the Hodge character and we show, using a result due to F. Bittner, that these can be constructed using classical pure Hodge theory only, sideskipping Deligne's construction of functorial mixed Hodge structures…

For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial…

The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such…

An invertible polynomial is a quasihomogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search…

We compute the stringy E function of the moduli space of rank 2 bundles over a Riemann surface of genus 3. In doing so, we answer a question of Batyrev about the stringy E functions of the GIT quotients of linear representations.

We compute the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and prove their positivity. This generalizes some results by G.C. Irelli [arXiv:0910.2592]. As an application we consider the…

The additive invariants of an algebraic variety is calculated in terms of those of the fixed point set under the action of additive and multiplicative groups, by using Bialynicki-Birula's fixed point formula for a projective algebraicset…

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g=3 into $ SL(2,C), and also of the moduli space of twisted representations. The case of genus g=1,2 has already been…

Let A be a Noetherian commutative ring. Assume that projective modules of rank r over polynomial extensions of A are extended from A. Then projective modules of rank r over discrete Hodge A-algebras are also extended from A. This result…

For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in arXiv:1203.2338 a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d+df, extending a definition of…

Let $X$ be an arbitrary smooth $n$-dimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes $c_1(X)c_{n-1}(X)$ depends only on the Hodge numbers of $X$. This result has been used by…

We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at…