Related papers: Toric Residues

Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra $A$ and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for…

Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint arXiv:math.AG/0306221. That is, they focus on the fact that toric…

In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or…

We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit $n$-dimensional cube onto itself, whose Jacobian is equal to $-1$ a.e. Moreover we prove that our homeomorphism can…

We generalize the toric residue mirror conjecture of Batyrev and Materov to not necessarily reflexive polytopes. Using this generalization we prove the toric residue mirror conjecture for Calabi-Yau complete intersections in Gorenstein…

We define the twisted affine Yangian of type $C$ and construct surjective homomorphisms from twisted affine Yangians of type $C$ to the universal enveloping algebra of the rectangular $W$-algebra associated with $\mathfrak{so}(ln)$ and a…

We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…

We give a geometrical construction of the canonical automorphic factor for the Jacobi group and construct new vector valued modular forms from Jacobi forms by differentiating them with respect to toroidal variables and then evaluating at…

Let R be an associative ring with identity. We study an elementary generalization of the classical Zariski topology, applied to the set of isomorphism classes of simple left R-modules (or, more generally, simple objects in a complete…

Any map of schemes $X\to Y$ defines an equivalence relation $R=X\times_Y X\to X\times X$, the relation of "being in the same fiber". We have shown elsewhere that not every equivalence relation has this form, even if it is assumed to be…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like…

Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$ denote the open subset parametrizing stable bundles. We show that if g>3 and n > 1,…

We study the structure of Jacobians of geometrically reduced curves over arbitrary (i. e., not necessarily perfect) fields. We show that, while such a group scheme cannot in general be decomposed into an affine and an Abelian part as over…

Let f_1,...,f_r be homogeneous polynomials in K[x_1,...,x_n], K a field. Put F=y_1f_1+...+y_rf_r in K[x,y] and let I be the ideal of K[x,y] generated by the partials of F relative to the x_i and y_j. The Jacobian ring of F is the quotient…

Given a hypersurface in a complex projective space, we prove that the multidegrees of its toric polar map agree, up to sign, with the coefficients of the Chern-Schwartz-MacPherson class of a distinguished open set, namely the complement of…

A toric degeneration in algebraic geometry is a process where a given projective variety is being degenerated into a toric one. Then one can obtain information about the original variety via analyzing the toric one, which is a much easier…

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We…

Let A be a principally polarized abelian threefold over a perfect field k, not isomorphic to a product over the algebraic closure of k. There exists a canonical extension k' of k, of degree 1 or 2, such that A becomes isomorphic to a…

We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…