Organizers: Andres Fernandez Herrero, Nathan Chen
Topic: Vector bundle methods and Brill Noether theory
Time: 4:30pm ET on Tuesdays, Fall 2022
Location: Room 520 (unless otherwise noted), Columbia math department
Here is a tentative schedule of the talks (these will be updated as we go along):
September 20 (Nathan Chen): Ample + nef: definitions, properties, examples. See 1.2-1.5 of [Positivity1] [notes]
September 27 (Amal Mattoo): Castelnuovo-Mumford regularity. See 1.8.A and parts of 1.8.B of [Positivity1]
October 4 (Gyujin Oh): Foundations of Brill Noether theory and Petri's condition. See Chapter V of [ACGH] and 3.1 of [VBtechniques]
October 11 (Matthew Hase-Liu): Brill-Noether theory on K3 surfaces and Lazarsfeld-Mukai bundles. See 3.2 and 3.3 of [VBtechniques]
October 18 (Benjamin Church): Mukai's theorem and proof of Brill-Noether-Petri. See 3.3 of [VBtechniques], first half of 3.4 -- stop at end of first proof of Theorem 3.2.1.(i).
October 25 (Simon Felten): Reider's theorem and stable bundles. See 4.1 and 4.2 of [VBtechniques]
November 1 (Andres Fernandez Herrero): Miyaoka's proof of Bogomolov's theorem. See 4.2 and 4.3 of [VBtechniques]
November 8 (Nicolas Vilches Reyes): Proof of Reider's theorem and applications. See 4.4 of [VBtechniques]
November 15 (Nathan Chen): Presenting a paper of Izzet Coskun, Eric Larson, Isabel Vogt: "The normal bundle of a general canonical curve of genus at least 7 is semistable".
November 22: Thanksgiving.
November 29 (Andres Fernandez Herrero): modern stability results of Langer.
References:
[ACGH] -- Geometry of algebraic curves volume 1 by Arbarello, Cornalba, Griffiths, Harris
Brill-Noether-Petri without degenerations. See https://www.math.stonybrook.edu/robert.lazarsfeld/Reprints/Lazarsfeld.BNP.pdf
[Positivity1] -- Positivity in algebraic geometry volume 1 by Lazarsfeld
[VBtechniques] -- A sampling of vector bundle techniques in the study of linear series by Lazarsfeld