Predonzan's Theorem establishes a necessary and sufficient condition in order that the Fano scheme parametrising all k-planes lying on a general complete intersection in a projective space is non-empty and, in this event, determines the dimension of this scheme. In this note we give a proof of this theorem following Predonzan's original idea.
On the Fano scheme of k-planes in a projective complete intersection
VALENZANO, Mario
2006-01-01
Abstract
Predonzan's Theorem establishes a necessary and sufficient condition in order that the Fano scheme parametrising all k-planes lying on a general complete intersection in a projective space is non-empty and, in this event, determines the dimension of this scheme. In this note we give a proof of this theorem following Predonzan's original idea.
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