Related papers: Residues in Toric Varieties

We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they…

In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that…

Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line…

This is a continuation of arXiv: 2408.03012. We answer affirmatively Question 5.10 posed in the previous article. More precisely, let $(X, \omega)$ be a conical symplectic variety of dimension $2n$ with $wt(\omega) = 2$, which has a…

In this paper we construct a spectral sequence computing a modified version of morphic cohomology of a toric variety (even when it is singular) in terms of combinatorial data coming from the fan of the toric variety.

We consider the action of a subtorus of the big torus on a toric variety. The aim of the paper is to define a natural notion of a quotient for this setting and to give an explicit algorithm for the construction of this quotient from the…

From a finite set in a lattice, we can define a toric variety embedded in a projective space. In this paper, we give a combinatorial description of the dual defect of the toric variety using the structure of the finite set as a Cayley sum…

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…

Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B_1, ..., B_k on X and integers m_1, ..., m_k, consider the line bundle L :=…

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of…

The space of non-resultant systems of bounded multiplicity for a toric variety X is a generalization of the space of rational curves on it. In our earlier work we proved a homotopy stability theorem and determined explicitly the homotopy…

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization…

Let G be a complex reductive group and X a projective spherical G-variety. Moreover, assume that the subalgebra A of the cohomology ring H^*(X, R) generated by the Chern classes of line bundles has Poincare duality. We give a description of…

Let $C$ be a genus one nodal curve over a local artinian base and let $E$ be a proper subcurve of genus one. We define residues for curves over local artinian rings, then define generalized residues with values in line bundles over the…

This paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor…

Given any toric subvariety $Y$ of a smooth toric variety $X$ of codimension $k$, we construct a length $k$ resolution of $\mathcal O_Y$ by line bundles on $X$. Furthermore, these line bundles can all be chosen to be direct summands of the…

We define conic reduction $X^{\mathrm{red}}_{\nu}$ for torus actions on the boundary $X$ of a strictly pseudo-convex domain and for a given weight $\nu$ labeling a unitary irreducible representation. There is a natural residual circle…

We present a counterexample to the conjecture of Bihan, Franz, McCrory, and van Hamel concerning the maximality of toric varieties. There exists a six dimensional projective toric variety X with the sum of the mod 2 Betti numbers of X(R)…

We prove a sheaf cohomology restriction (SCORE) formula for a class of vector bundles on complete intersections in toric varieties. The formula enables one to compute cohomology products on the complete intersection $X$ via computations on…

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…