Giancarlo Urzua (FRIAS):
On one of the ends of MMP: Markovian planes
Zeit und Ort
Freitag, 20.10.23, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Zusammenfassung
About a year ago, I gave a talk at this seminar on degenerations of surfaces with Wahl singularities. I tried by then to explain the explicit birational picture and some connections with exceptional collections of vector bundles. We see in this Mori theory divisorial contractions and flips controlled by Hirzebruch-Jung continued fractions (a summary can be found here https://arxiv.org/abs/1311.4844). As final products of this MMP, we arrive at either nef canonical class, smooth deformations of ruled surfaces, and degenerations of the projective plane (compare with the classical MMP for nonsingular projective surfaces). In this talk, I would like to explain these "Markovian planes". The name comes from the classification of such degenerations , due to Hacking and Prokorov 2010 (after Badescu and Manetti), as partial smoothings of P(a^2,b^2,c^2) where (a,b,c) satisfies the Markov equation x^2+y^2+z^2=3xyz. It turns out that there is a beautiful birational picture behind them, which in particular gives new insights to Markov's uniqueness conjecture. This is a joint work in progress together with Juan Pablo Zúñiga (Ph.D. student at UC Chile). \n\n