Points on Rational Normal Curves and the ABCT Variety

Fuente: arXiv
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Auteurs principaux: Agostini, Daniele, Ramesh, Lakshmi, Shen, Dawei
Format: Preprint
Publié: 2024
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author Agostini, Daniele
Ramesh, Lakshmi
Shen, Dawei
author_facet Agostini, Daniele
Ramesh, Lakshmi
Shen, Dawei
contents The ABCT variety is defined as the closure of the image of $G(2,n)$ under the Veronese map. We realize the ABCT variety $V(3,n)$ as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the fundamental class of $V(3,n)$. As an application, we show that special Schubert coefficients of this class are given by Eulerian numbers, matching a formula by Cachazo-He-Yuan. On the way to this, we prove that the variety of configuration of points on a common divisor on a smooth variety is reduced and irreducible, generalizing a result of Caminata-Moon-Schaffler.
format Preprint
id arxiv_https___arxiv_org_abs_2412_12514
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Points on Rational Normal Curves and the ABCT Variety
Agostini, Daniele
Ramesh, Lakshmi
Shen, Dawei
Algebraic Geometry
Mathematical Physics
Combinatorics
05E05, 14J81, 14N05, 14N15, 14N20
The ABCT variety is defined as the closure of the image of $G(2,n)$ under the Veronese map. We realize the ABCT variety $V(3,n)$ as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the fundamental class of $V(3,n)$. As an application, we show that special Schubert coefficients of this class are given by Eulerian numbers, matching a formula by Cachazo-He-Yuan. On the way to this, we prove that the variety of configuration of points on a common divisor on a smooth variety is reduced and irreducible, generalizing a result of Caminata-Moon-Schaffler.
title Points on Rational Normal Curves and the ABCT Variety
topic Algebraic Geometry
Mathematical Physics
Combinatorics
05E05, 14J81, 14N05, 14N15, 14N20
url https://arxiv.org/abs/2412.12514