Back to Algebraic Geometry Seminar: Fall 2017
Algebraic Geometry Seminar
Date: Tuesday, Sep 19, 2017
Time: 3:30PM - 4:30PM
Location: LCB 215
Daniel Bragg
University of Washington
Title |
Supersingular twistor lines |
Abstract |
Supersingular K3 surfaces are a remarkable class of varieties that exhibit many unique features of positive characteristic algebraic geometry. We will give a new construction of certain one-parameter families of (twisted) supersingular K3 surfaces, which we call supersingular twistor lines. This will entail a detailed examination of the Brauer group, together with techniques coming from the derived category and Fourier–Mukai equivalences. We will show how these families are a powerful tool in the study of supersingular K3 surfaces, yielding relatively short proofs of Ogus’ crystalline Torelli theorem, Rudakov–Shafarevich’s results on degenerations of supersingular K3 surfaces, and Shioda’s conjecture on unirationality. As a byproduct, we extend these results to a wider range of characteristics than was previously known. |
Algebraic Geometry