We give a constructive proof of a classical theorem which determines irreducible plane curves that are contractible to a point by a Cremona transformation. The problem of characterizing Cremona contractible (not necessarily irreducible) hypersurfaces in a projective space is in general widely open: we report on the only known result about reducible plane curves consisting of two components, due to litaka, and we discuss a couple of examples concerning plane curves with more components. Finally, we prove that all varieties of codimension at least two in a projective space are Cremona contractible to a point.
On Cremona contractibility
CALABRI, Alberto;
2013
Abstract
We give a constructive proof of a classical theorem which determines irreducible plane curves that are contractible to a point by a Cremona transformation. The problem of characterizing Cremona contractible (not necessarily irreducible) hypersurfaces in a projective space is in general widely open: we report on the only known result about reducible plane curves consisting of two components, due to litaka, and we discuss a couple of examples concerning plane curves with more components. Finally, we prove that all varieties of codimension at least two in a projective space are Cremona contractible to a point.File in questo prodotto:
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