Seminar Algebra and Geometry: Alberto Calabri (Università di Ferrara)

On Cremona contractibility of plane curves

A plane curve C is said to be Cremona contractible if there exists a plane Cremona transformation that contracts C to a point. A characterization of irreducible plane curves which are Cremona contractible is a classical result due to Castelnuovo and Enriques in 1900 and that has been improved by Kumar and Murthy in 1982. The case of two irreducible components is due to Iitaka in 1988. After reviewing these results, we will discuss the open problem of characterizing reducible (reduced) plane curves which are Cremona contractible. In particular we will deal with reduced unions of lines and we will give a classification in case the lines are at least 12.

This is a joint work in progress with Ciro Ciliberto (Univ. Roma "Tor Vergata").

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