Related papers: Anticanonical modules of Segre products

We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

In this paper, we complete the classification of the {\bf Z}-graded modules of the intermediate series over the $q$-analog Virasoro-like algebra $L$. We first construct four classes of irreducible {\bf Z}-graded $L$-modules of the…

We present a method to compute the degrees of the Segre classes of a subscheme of complex projective space. The method is based on generic residuation and intersection theory. It has been implemented using the software system Macaulay2.

For any grading by an abelian group $G$ on the exceptional simple Lie algebra $\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple…

We prove a sharp bound for the average value of the triple product of modular functions for the Hecke subgroup \Gamma_0(N). Our result is an extension of the main result in {Bernstein&Reznikov-2004} to a fixed cuspidal representation of the…

Let T be an involution of the finite dimensional complex reductive Lie algebra g and g=k+p be the associated Cartan decomposition. Denote by K the adjoint group of k. The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m},…

Let U be the complement of a smooth anticanonical divisor in a del Pezzo surface of degree at most 7 over a number field k. We show that there is an effective uniform bound for the size of the Brauer group of U in terms of the degree of k.

We study Veronese and Segre morphisms between non-commutative projective spaces. We compute finite reduced Gr\"obner bases for their kernels, and we compare them with their analogues in the commutative case.

We classify a class of infinite-dimensional simple graded pre-Lie algebras on the graded vector space underlying the algebra of Laurent polynomials, with a specific form for the product.

This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In…

Khovanov-Lauda-Rouquier algebras $R_\theta$ of finite Lie type are affine quasihereditary with standard modules $\Delta(\pi)$ labeled by Kostant partitions $\pi$ of $\theta$. In type $A$, we construct explicit projective resolutions of…

This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where…

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…

We prove that a product of $m>5$ copies of $\PP^1$, embedded in the projective space $\PP^r$ by the standard Segre embedding, is $k$-identifiable (i.e. a general point of the secant variety $S^k(X)$ is contained in only one $(k+1)$-secant…

Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of a holomorphic PDE system defining the Segre family of a real analytic hypersurface. This gives a new proof of some well known results of CR…

To every regular category $\mathcal{A}$ equipped with a degree function $\delta$ one can attach a pseudo-abelian tensor category $\mathcal{T}(\mathcal{A},\delta)$. We show that the generating objects of $\mathcal{T}$ decompose canonically…

We study the x- and y-regularity of a bigraded K-algebra R. These notions are used to study asymptotic properties of certain finitely generated bigraded modules. As an application we get for any equigenerated graded ideal I upper bounds for…

In this article we compute a minimal Groebner basis for the symmetric algebra for certain affine Monomial Curves, as an R-module. Keywords: Monomial Curves, Groebner Basis, Symmetric Algebra. Mathematics Subject Classification 2000: 13P10,…

We compute the automorphism groups of some quantized algebras, including tensor products of quantum Weyl algebras and some skew polynomial rings.