Polarity with respect ot a foliation and Cayley-Bacharach Theorems
A Campillo, J Olivares - 2001 - degruyter.com
2001•degruyter.com
We prove that a foliation of degree different from one on the projective plane (de® ned over
any algebraically closed ground® eld), is uniquely determined by its subscheme of singular
points (which we call the singular subscheme of the foliation). Conversely, we provide three
different characterizations of those subschemes that are the singular subscheme of some
foliation.
any algebraically closed ground® eld), is uniquely determined by its subscheme of singular
points (which we call the singular subscheme of the foliation). Conversely, we provide three
different characterizations of those subschemes that are the singular subscheme of some
foliation.
Abstract
We prove that a foliation of degree different from one on the projective plane (de® ned over any algebraically closed ground® eld), is uniquely determined by its subscheme of singular points (which we call the singular subscheme of the foliation). Conversely, we provide three different characterizations of those subschemes that are the singular subscheme of some foliation.
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