Work

On Hilbert scheme of complete intersection on the biprojective

Year: 2026

Type: article

Abstract: The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $$ X = \mathbb {P}^m \times \mathbb {P}^n $$ X = P m × P n . For this purpose, we define a partial order on the bidegrees of the bihomogeneous forms. As a consequence of this construction, we provide an explicit computation of the Hilbert scheme for curves of genus 7 and 8 listed in [1] and [11] that are complete intersections. Finally, we construct the coarse moduli space of canonical complete intersections in $$ \mathbb {P}^m \times \mathbb {P}^n $$ P m × P n .

Source: Geometriae Dedicata

DOI: 10.1007/s10711-026-01098-7

Authors: Aislan Leal Fontes, Maxwell da Paixão de Jesus Santos

Institution: Universidade Federal de Sergipe

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,090

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Universidade Federal de Sergipe