Related papers: Virtual Resolutions of Monomial Ideals on Toric Va…

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…

Extending the notion of indispensable binomials of a toric ideal, we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for…

We answer positively a question of B. Teissier on existence of resolution of singularities inside an equivariant map of toric varieties.

We show that ideal submodules and closed ternary ideals in Hilbert modules are the same. We use this insight as a little peg on which to hang a little note about interrelations with other notions regarding Hilbert modules. In Section 3, we…

In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…

In this work we construct global resolutions for general coherent equivariant sheaves over toric varieties. For this, we use the framework of sheaves over posets. We develop a notion of gluing of posets and of sheaves over posets, which we…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

Let $X=(x_{ij})$ and $Y=(y_{ij})$ be generic $n$ by $n$ matrices and $Z=XY-YX$. Let $S=k[x_{11},...,x_{nn},y_{11},...,y_{nn}]$, where $k$ is a field, let $I$ be the ideal generated by the entries of $Z$ and let $R=S/I$. We give a conjecture…

We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples…

We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of…

We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum…

We develop an analogue of Eisenbud-Floystad-Schreyer's Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier- Mukai transform, works quite generally and provides a new perspective…

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by…

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…

Suppose that $f: Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y'\to Y$ and $X'\to X$ to obtain an induced…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.

The $G$-representation variety $R_G(\Sigma_g)$ parametrizes the representations of the fundamental groups of surfaces $\pi_1(\Sigma_g)$ into an algebraic group $G$. Taking $G$ to be the groups of $n \times n$ upper triangular or unipotent…

In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…

Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that…

We present an explicit construction of a minimal cellular resolution for the edge ideals of forests, based on discrete Morse theory. In particular, the generators of the free modules are subsets of the generators of the modules in the…