Seminar Algebra and Geometry: Sara Durighetto (Ferrara)

Birational geometry of pairs

Let C, D be two birational subvarieties of the projective space Pⁿ. I am interested in understanding when there exists a Cremona modification f:  Pⁿ --->Pⁿ  such that  f(C) = D. For the sake of this talk I will restrict to a configuration of lines in P². In this special case I'll suggest a classification of configurations of lines that are contractible to a bunch of points. In doing this I will propose an unexpected configuration that seems to violate an established conjecture.

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