相关论文: Multiplier modules, $V$-filtrations and Bernstein-…

Let X be a smooth projective variety and let G be a connected reductive group, both defined over a field of characteristic 0. Given a faithful representation $\rho$ of G into a product of general linear groups, we define a moduli stack of…

We explicitly compute the Hodge ideals of Q-divisors in terms of the V-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and…

In this article we introduce the mixed Hodge structure of the Brieskorn module of a polynomial $f$ in $\C^{n+1}$, where $f$ satisfies a certain regularity condition at infinity (and hence has isolated singularities). We give an algorithm…

We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions X_s to positive characteristic such that the action of the Frobenius morphism on the top…

P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study…

Let $K$ be a global field and let $Z$ be a geometrically irreducible algebraic variety defined over $K$. We show that if a big set $S\subseteq Z$ of rational points of bounded height occupies few residue classes modulo $\mathfrak{p}$ for…

In this survey we provide an overview of some recent developments in the construction of moduli spaces using stack-theoretic techniques. We will also explain the analogue of Harder-Narasimhan stratifications for general stacks, known as…

We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the…

Let X be a smooth variety and J, K two ideal sheaves on X. We prove the following formula relating the multiplier ideals of J, K and J+K: I(X, c(J+K))\subset \sum_{a+b=c} I(X, aJ)\cdot I(X,bK). An analogous formula holds for the asymptotic…

In characteristic zero, the Bernstein-Sato polynomial of a hypersurface can be described as the minimal polynomial of the action of an Euler operator on a suitable D-module. We consider the analogous D-module in positive characteristic, and…

In this paper, we introduce geometric multiplicities, which are positive varieties with potential fibered over the Cartan subgroup $H$ of a reductive group $G$. They form a monoidal category and we construct a monoidal functor from this…

We extend the dimension and strong linearity results of generic vanishing theory to bundles of holomorphic forms and rank one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated to irregular…

We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…

Let $G$ be a finite group and let $k$ be a field of characteristic $p$. It is known that a $kG$-module $V$ carries a non-degenerate $G$-invariant bilinear form $b$ if and only if $V$ is self-dual. We show that whenever a Morita bimodule $M$…

In this paper we continue our study of modules satisfying the prime radical condition ($\mathbb{P}$-radical modules), that was introduced in Part I (see \cite{BS}). Let $R$ be a commutative ring with identity. The purpose of this paper is…

We introduce a Grassmannian structure for a class of quotient Hilbert modules and attack the polydisc version of Arveson-Douglas conjecture associated to distinguished varieties. More interestingly, we obtain an operator-theoretic…

Let $G$ be a linearly reductive group acting on a vector space $V$, and $f$ a (semi-)invariant polynomial on $V$. In this paper we study systematically decompositions of the Bernstein-Sato polynomial of $f$ in parallel with some…

We investigate Fourier multipliers with smooth symbols defined over locally compact Hausdorff groups. Our main results in this paper establish new H\"ormander-Mikhlin criteria for spectral and non-spectral multipliers. The key novelties…

In this article we extend a previous definition of Castelnuovo-Mumford regularity for modules over an algebra graded by a finitely generated abelian group. Our notion of regularity is based on Maclagan and Smith's definition, and is…