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arXiv · 2411.12546

On Hilbert scheme of complete intersection on the biprojective

Aislan Leal Fontes·Maxwell Paixão
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Abstract

The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $X=\mathbb{P}^m\times\mathbb{P}^n$ and for this, we define a partial order on the bidegrees of the bihomogeneous forms. As a consequence of this construction, we computer explicitly the Hilbert scheme for curves of genus 7 and 8 listed in \cite{MUK95} and \cite{MUKIDE03} that are complete intersections. Finally, we construct the coarse moduli space of complete intersections in $\mathbb{P}^1\times\mathbb{P}^1$.

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Aislan Leal Fontes, Maxwell Paixão. 2025-07-08. On Hilbert scheme of complete intersection on the biprojective. https://arxiv.org/abs/2411.12546

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