Points on Rational Normal Curves and the ABCT Variety

Daniele Agostini; Lakshmi Ramesh; Dawei Shen

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arXiv · 2412.12514

Points on Rational Normal Curves and the ABCT Variety

Daniele Agostini·Lakshmi Ramesh·Dawei Shen

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Abstract

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.

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BibTeX RIS

Daniele Agostini, Lakshmi Ramesh, Dawei Shen. 2024-12-17. Points on Rational Normal Curves and the ABCT Variety. https://arxiv.org/abs/2412.12514

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