Related papers: Translation quiver varieties
Consider independent fair coin-flips at each site of the lattice Z^d. A translation-equivariant matching rule is a perfect matching of heads to tails that commutes with translations of Z^d and is given by a deterministic function of the…
Machine translation systems are expected to cope with various types of constraints in many practical scenarios. While neural machine translation (NMT) has achieved strong performance in unconstrained cases, it is non-trivial to impose…
This is an expository paper in which we define projective GIT quotients and introduce toric varieties from this perspective. It is intended primarily for readers who are learning either invariant theory or toric geometry for the first time.
We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient algebras of the form $A = \kk Q/I$, where $Q$ is a quiver and $I$ is an ideal of relations coming from taking partial derivatives of a twisted…
We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with…
We study translative integral formulas for certain translation invariant functionals on convex polytopes and discuss local extensions and applications to Poisson processes and Boolean models.
Some diophantine aspects of projective toric varieties: We present several faces of projective toric varieties, of interest from the point of view of diophantine geometry. We make explicit the theory on a number of meaningful examples and…
We give an inductive proof that the generalized Severi varieties -- the varieties which parametrize (irreducible) plane curves of given degree and genus, with a fixed tangency profile to a given line at several general fixed points and…
In this paper, we give an explicit description of holomorphic polyvector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties.
We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.
Although attention-based Neural Machine Translation (NMT) has achieved remarkable progress in recent years, it still suffers from issues of repeating and dropping translations. To alleviate these issues, we propose a novel key-value…
Smooth projective $\mathbb{G}_m$-varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting formula of such motives, which reduces the computation of their Chow-Witt groups to…
We study the algebraic symplectic geometry of multiplicative quiver varieties, which are moduli spaces of representations of certain quiver algebras, introduced by Crawley-Boevey and Shaw, called multiplicative preprojective algebras. They…
We study quivers supporting twisted graded Calabi-Yau algebras, building on work of Rogalski and the first author. Specifically, we classify quivers on four vertices in which the Nakayama automorphism acts on the degree zero part by either…
A pathway from one vertex of a quiver to another is a reduced path. We modify the classical definition of quiver representations and we prove that semi-invariant polynomials for filtered quiver representations come from diagonal entries if…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
We consider representation spaces of quivers, together with their base change action, and classify the spherical varieties among them.
We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective…