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arXiv · 2411.14232

Counting 3-uple Veronese surfaces

Anand Deopurkar·Anand Patel
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Abstract

This paper culminates in the count of the number of 3-Veronese surfaces passing through 13 general points. This follows the case of 2-Veronese surfaces discovered by Coble in the 1920's. One important element of the calculation is a direct construction of a space of "complete triangles." Our construction is different from the classical ordered constructions of Schubert, Collino and Fulton, as it occurs directly on the Hilbert scheme of length 3 subschemes of the plane. We transport the enumerative problem into a 26-dimensional Grassmannian bundle over our space of complete triangles, where we perform Atiyah-Bott localization. Several important questions arise, which we collect at the end of the paper.

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Anand Deopurkar, Anand Patel. 2024-11-21. Counting 3-uple Veronese surfaces. https://arxiv.org/abs/2411.14232

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