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On the Ideal of Veronesean Surfaces

Published online by Cambridge University Press:  20 November 2018

A. Gimigliano  and
A. Lorenzini
A. Gimigliano
Affiliation:
Dipartimento di Matematica, Via L. B. Alberti, 4, 16132 Genova, Italy
A. Lorenzini
Affiliation:
Dipartimento di Matematica, Via Vanvitelli, 1, 06100 Perugia, Italy
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Abstract

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We consider the blowing up of ℙ2 at s sufficiently general distinct points and its projective embedding by the linear system of the curves of a given degree through the points. We study the ideal of the resulting (Veronesean) surface and find that it can be described by two matrices of linear forms, in the sense that it is generated by the entries of the product matrix and the minors of complementary orders of the two matrices.

By cutting the surface twice with general hyperplanes, we also obtain some information about the generation (or even the resolution) of certain classes of points in projective space.

Keywords

14J2614M05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 758 - 777
Copyright
Copyright © Canadian Mathematical Society 1993

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