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Homaloidal nets and ideals of fat points I

Published online by Cambridge University Press:  01 March 2016

Zaqueu Ramos
Affiliation:
Departamento de Matemática, CCET, Universidade Federal de Sergipe, 49100-000 São Cristovão, Sergipe, Brazil email [email protected]
Aron Simis
Affiliation:
Departamento de Matemática, CCEN, Universidade Federal de Pernambuco, 50740-560 Recife, PE, Brazil Departamento de Matemática, CCEN, Universidade Federal da Paraíba, 58059-900 João Pessoa, PB, Brazil email [email protected]

Abstract

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We consider plane Cremona maps with proper base points and the base ideal generated by the linear system of forms defining the map. The object of this work is to study the link between the algebraic properties of the base ideal and those of the ideal of these points fattened by the virtual multiplicities arising from the linear system. We reveal conditions which naturally regulate this association, with particular emphasis on the homological side. While most classical numerical inequalities concern the three highest virtual multiplicities, here we emphasize also the role of one single highest multiplicity. In this vein we describe classes of Cremona maps for large and small values of the highest virtual multiplicity. We also deal with the delicate question as to when is the base ideal non-saturated and consider the structure of its saturation.

Type
Research Article
Copyright
© The Author(s) 2016 

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