March 12, 2024Open Access

Secant variety and syzygies of Hilbert scheme of two points

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Abstract

In this paper, we prove that the singular locus of Sec (X^2) coincides with X^2 under the Grothendieck-Pl\"ucker embedding X^2 PN when X is embedded by a 4-very ample line bundle. We also prove that the embedding X^2 PN satisfies Green's condition (Nₚ) when the embedding of X is positive enough. As an application, we describe the geometry of a resolution of singularities from the secant bundle to Sec (X^2) when X is a surface.

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Yoon et al. (Tue,) studied this question.

synapsesocial.com/papers/68e747e6b6db6435876c0d59 https://doi.org/https://doi.org/10.48550/arxiv.2403.07315

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