Related papers: On Hilbert covariants

Given a Hilbert cuspidal newform $g$ we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted $L$-series of $g$ by fundamental discriminants. The family is parametrized…

This paper is about sheaf cohomology for varieties (schemes) in characteristic $p>0$. We assume the presence of a Frobenius splitting. (See V.B. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties,…

Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. In this article we study quotient Hilbert modules obtained from submodules,…

Let g be a basic classical Lie superalgebra over C. In the case of a typical weight whose every nonnegative integer multiple is also typical, we compute a closed form for the Hilbert series whose coefficients encode the dimensions of…

Fix integers $a\geq 1$, $b$ and $c$. We prove that for certain projective varieties $V\subset{\bold P}^r$ (e.g. certain possibly singular complete intersections), there are only finitely many components of the Hilbert scheme parametrizing…

We study the \'etale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theorem: in the "generic" case, the cohomology with torsion…

Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…

Let $E$ be a vector bundle and $L$ be a line bundle over a smooth projective variety $X$. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form $H^{p,q}(X,\SSS^{\alpha}E\otimes \wedge^{\beta}…

Let $W$ be a finite-dimensional representation of a reductive algebraic group $G$. The invariant Hilbert scheme $\mathcal{H}$ is a moduli space that classifies the $G$-stable closed subschemes $Z$ of $W$ such that the affine algebra $k[Z]$…

Schubert coefficients are nonnegative integers $c^w_{u,v}$ that arise in Algebraic Geometry and play a central role in Algebraic Combinatorics. It is a major open problem whether they have a combinatorial interpretation, i.e, whether…

For $G$ a finite group acting linearly on $\mathbb{A}^2$, the equivariant Hilbert scheme $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ is a natural resolution of singularities of $\operatorname{Sym}^r(\mathbb{A}^2/G)$. In this paper we study the…

The Hilbert class polynomial has as roots the j-invariants of elliptic curves whose endomorphism ring is a given imaginary quadratic order. It can be used to compute elliptic curves over finite fields with a prescribed number of points.…

Let $F$ be a totally real field and let $S$ denote the geometric special fiber of a Hilbert modular variety associated to $F$, at a prime unramified in $F$. We show that the order of vanishing of the Hasse invariant on $S$ is equal to the…

Given an embedded smooth projective variety Y in CP^n, we show how the existence of a hypersurface with high multiplicity along Y, but of relatively low degree and log canonical near Y implies vanishing of higher cohomology for certain…

The diagonal in a product of projective spaces is cut out by the ideal of 2x2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally…

We consider a finite dimensional $\kk G$-module $V$ of a $p$-group $G$ over a field $\kk$ of characteristic $p$. We describe a generating set for the corresponding Hilbert Ideal. In case $G$ is cyclic this yields that the algebra $\kk[V]_G$…

Let $G$ be a simple graph on $n$ vertices, and let $J_G$ denotes the corresponding binomial edge ideal in $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$, where $\mathbb{K}$ is a field. We show that if a vertex satisfies a certain degree…

We use representation theory and Bott's theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Pl\"ucker embedding. As a biproduct we answer a question of Wahl about the…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…