The premise of this seminar is simple: pick a classic paper in algebraic geometry, where the definitions of "classic paper" and "algebraic geometry" are up to you. (The organizers may try to talk you out of it if they disagree.) Give a talk or two on said paper. Repeat. The goal is to get a flavor for what the results and new ideas are, but not necessarily to go through all the details.

Some guidelines: the paper should be post-EGA and reasonably accessible to graduate students. If the paper is very long or complicated, consider focusing on a single idea, or pick a different paper. Avoid papers that have already been discussed in detail in other seminars in recent memory. Talks should attempt to be self-contained; in particular, they shouldn't rely on anything discussed in talks on other papers. Try to give the background necessary for understanding the paper. If you split your exposition into two talks, consider pushing the most technical parts to the second one.

Suggested Papers: See here. For an arbitrary and unofficial list of additional ideas, see below. More suggestions are welcome, though this list may be removed if it becomes too contentious, distracting, unwieldy, or any combination thereof.

- [ACV] Abramovich-Corti-Vistoli, Twisted Bundles and Admissible Covers
- [A] Atiyah, Vector Bundles over an Elliptic Curve
**claimed by Galya** - [CG] Clemens-Griffiths, The Intermediate Jacobian of a Cubic Threefold
- [F] Fontaine, Il n'y a pas de variété abélienne sur Z
**claimed by Qixiao** - [HMP] Harris-Mazur-Pandharipande, Hypersurfaces of Low Degree
- [HM] Harris-Mumford, On the Kodaira Dimension of the Moduli Space of Curves
- [Ha] Hartshorne, Connectedness of the Hilbert Scheme
- [Ho] Honda, Isogeny Classes of Abelian Varieties over Finite Fields
- [dJ] de Jong, Smoothness, Semi-stability, and Alterations
**claimed by Remy** - [MM] Mori-Mukai, The Uniruledness of the Moduli Space of Curves of Genus 11
- [M] Mumford, Picard Groups of Moduli Problems
- [ST] Serre-Tate, Good Reduction of Abelian Varieties
**claimed by Shizhang** - [V] Vakil, Murphy's Law in Algebraic Geometry: Badly Behaved Deformation Spaces
**claimed by Raymond**

Please e-mail the organizers if you'd like to receive notifications, or to volunteer for a talk.

**Organizers:** Raymond Cheng, Carl Lian.

**Time and location:** Tuesdays at 1:30 PM in Math 407

Date | Speaker | Paper |
---|---|---|

30 May | Sam Mundy | Mazur, Rational Points of Abelian Varieties with Values in Towers of Number Fields |

6 June | Remy van Dobben de Bruyn | de Jong, Smoothness, Semi-stability, and Alterations |

13 June | Shuai Wang | Horrocks-Mumford, A Rank 2 Bundle on P4 with 15,000 Symmetries |

20 June | Daniel Gulotta | Dwork, On the Rationality of the Zeta Function of an Algebraic Variety |

27 June | Daniel Gulotta | (cont.) |

4 July | No Talk: Independence Day | |

11 July | cancelled | |

18 July | Shizhang Li | Serre-Tate, Good Reduction of Abelian Varieties |

25 July | Carl Lian | Caporaso-Harris, Counting Plane Curves of Any Genus |

1 August | No Talk: Stacks Project Workshop | |

8 August | Qixiao Ma | Fontaine, Il n'y a pas de variété abélienne sur Z |