Seminari del Dipartimento di Matematica

Seminario del 2025

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.