Related papers: Translation quiver varieties
It has been recently shown that the iteration of Nash modification on not necessarily normal toric varieties corresponds to a purely combinatorial algorithm on the generators of the semigroup associated to the toric variety. We will show…
The goal of this paper is to establish Beilinson-Bernstein type localization theorems for quantizations of some conical symplectic resolutions. We prove the full localization theorems for finite and affine type A Nakajima quiver varieties.…
An oblivious point on a translation surface is a point with no closed geodesic passing through it. Nguyen, Pan, and Su (2017) showed that there are at most finitely many oblivious points on any given translation surface and constructed a…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be…
Previous work on multimodal machine translation (MMT) has focused on the way of incorporating vision features into translation but little attention is on the quality of vision models. In this work, we investigate the impact of vision models…
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the…
By the work of Hernandez-Leclerc, Leclerc-Plamondon, and Keller-Scherotzke, affine graded Nakajima quiver varieties associated with a Dynkin quiver $Q$ admit an algebraic description in terms of modules over the singular Nakajima category…
Neural machine translation models usually adopt the teacher forcing strategy for training which requires the predicted sequence matches ground truth word by word and forces the probability of each prediction to approach a 0-1 distribution.…
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.
This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety M_\vartheta(Q,r) of a finite acyclic quiver Q (with a unique source) and a…
Large language models have demonstrated the capability to perform on machine translation when the input is prompted with a few examples (in-context learning). Translation quality depends on various features of the selected examples, such as…
This paper proposes an analysis of classifiers into four major types: UNIT, METRIC, GROUP and SPECIES, based on properties of both Japanese and English. The analysis makes possible a uniform and straightforward treatment of noun phrases…
We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.
Unlike classical lexical overlap metrics such as BLEU, most current evaluation metrics for machine translation (for example, COMET or BERTScore) are based on black-box large language models. They often achieve strong correlations with human…
Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers -- a type of directed multigraph with significant relevance in algebra, combinatorics,…
In this paper we show that quotients of smooth projective toric varieties by $\mu_p$ in positive characteristics $p$ are toric varieties.
We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with…
For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups…
We present and expand some existing results on the Zariski closure of cyclic groups and semigroups of matrices. We show that, with the exclusion of isolated points, their irreducible components are toric varieties. Additionally, we…