Seminario del 2025

Marzo
18
2025
Bruno Dewer
Divisorial elementary Mori contractions of maximal length
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
algebra e geometria
An elementary Mori contraction from a smooth variety X is a morphism with connected fibres onto a normal variety which contracts a single extremal ray of K_X-negative curves. Thanks to a result by P. Ionescu and J. Wisniewsi, we know that the length of such a contraction (i.e. the minimal degree -K_X can have on contracted rational curves) is bounded from above. In a paper which dates back to 2013, A. Höring and C. Novelli studied elementary Mori contractions of maximal length, that is, elementary Mori contractions for which the upper bound is met. Their main result exhibits the structure of a projective bundle for the locus of positive-dimensional fibres up to a birational modification. In my talk, I will move to the submaximal case, in other words the case where the length equals its upper bound minus one, and focus on the divisorial case.
organizzato da: Federico Tufo
nell'ambito del Progetto P.R.I.N. PRIN 2022 MONGARDI (CUP J53D23003840006) del prof. Giovanni Mongardi

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