Related papers: Irreducible components of Toric Complete Intersect…

We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating equivariant Hirzebruch genera of torus-invariant Cartier…

We introduce toric $b$-divisors on complete smooth toric varieties and a notion of integrability of such divisors. We show that under some positivity assumptions toric $b$-divisors are integrable and that their degree is given as the volume…

Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic vector bundle on X. We prove that E admits an equivariant structure if and only if E admits a…

We show, under some natural conditions, that the set of abelian points on the non-anomalous subset of a closed irreducible subvariety $X$ intersected with the union of connected algebraic subgroups of codimension at least $\dim X$ in a…

Given $\mathbf{n}=(n_{1},\ldots,n_{r})\in\mathbb{N}^r$, let $\Gamma_{\mathbf{n}}$ be a group presentable as $$\left\langle \gamma_{1},\ldots,\gamma_{r}\:|\:\gamma_{1}^{n_{1}}=\gamma_{2}^{n_{2}}=\cdots=\gamma_{r}^{n_{r}}\right\rangle. $$ If…

Given any polynomial system with fixed monomial term structure, we give explicit formulae for the generic number of roots with specified coordinate vanishing restrictions. For the case of affine space minus an arbitrary union of coordinate…

In this note we study linear systems on complete toric varieties $X$ with an invariant point, whose orbit under the action of the automorphism group of $X$ contains the dense torus $T$ of $X$. We give a characterization of such varieties in…

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme…

The moduli space of stable surfaces with $K_X^2 = 1$ and $\chi(X) = 3$ has at least two irreducible components that contain surfaces with T-singularities. We show that the two known components intersect transversally in a divisor. Moreover,…

The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete…

Let $M$ be a smooth complex projective toric variety equipped with an action of a torus $T$, such that the complement $D$ of the open $T$--orbit in $M$ is a simple normal crossing divisor. Let $G$ be a complex reductive affine algebraic…

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations defined from a suitable filtration of the Weyl algebra $A_{n}(k)$. This generalizes an important…

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference…

We discuss conditions for complete intersections in a toric variety which allow to compute Hodge numbers if the complete intersection is a quasi-smooth complete variety. A preliminary step is the computation of the Euler characteristic of…

Differently from the Milnor number, no formula relating the Tjurina number of a reducible algebroid curve to invariants of its branches was known. The aim of this work is to provide such a formula for a complete intersection algebroid curve…

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…

We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric…

In this paper, an intersection theory for generic differential polynomials is presented. The intersection of an irreducible differential variety of dimension $d$ and order $h$ with a generic differential hypersurface of order $s$ is shown…

For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in…

We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application…