Esquema de Hilbert para três pontos em P^2 (HILB^3 P^2 )

Abstract

In this work we will present a study of 3-conic linear systems in S =k[x; y; z], also called conic networks. Our focus is on characterizing the family of conics that pass through three points in P2. Such networks of conics are of the determinant type, which means that they come from the smallest maximals of a 3 × 2 matrix whose entries are linear forms. We intend this relatively simple case study, to illustrate the ideas around the construction of spaces with parameters for families of algebraic varieties. We will describe the space, in an area, in a coordinate area of dimension 3 of space, in a coordinate area of dimension 3 of spacemann, in a coordinate area of conic dimension. We show that D is nonsingular and that its spread along the orbit of redex^2; xy; x>z plunging into G(7; 10) and identifying Hilb3P2, the desired space for the family of unordered triples in P2.