Organized by Noah Olander and Song Yu at the Department of Mathematics, Columbia University

Time and location: Thursdays 2:30-4:00pm, 507 Mathematics

The goal of this reading seminar is to learn intersection theory in the style of a topics course. We will mostly follow William Fulton's classical book *Intersection Theory*. We will first go over the foundational setup of the subject (Chapters 1-8 of Fulton), and then move on to a selection of more involved results and applications from the remaining chapters and literature.

Please email the organizers if you wish to join the mailing list.

Special thanks to Henry Liu and Michael Zhao for live-TeXing notes for the seminar. Here are Henry's notes and here are Michael's notes.

## References and Resources

- William Fulton,
*Intersection Theory*, Springer-Verlag New York, 1998. (available through SpringerLink) - William Fulton,
*Introduction to Intersection Theory in Algebraic Geometry*, Regional Conference Series in Mathematics, No. 54, AMS, 1984.- These are notes from expository lectures given by Fulton introducing his approach to intersection theory.

- The webpage of Ravi Vakil's course on intersection theory, including his notes.
- Videos of Barbara Fantechi's course on intersection theory (notes by a student).
- [L] Carl Lian,
*The Class of the d-elliptic Locus in Genus 2*. - [M] David Mumford,
*Towards an Enumerative Geometry of the Moduli Space of Curves*.- In the last two talks, Carl will explain Mumford's description of the Chow ring of the moduli space of curves (in low genus) in terms of the tautological classes, and a computational application of his own in genus 2.

## Schedule

Date | Speaker | Title | Reference |
---|---|---|---|

Sept 13 | Song Yu | Rational Equivalence | §1 |

Sept 20 | Noah Olander | Divisors | §2 |

Sept 27 | Alex Pieloch | Vector Bundles and Chern Classes | §3 |

Oct 4 | Song Yu | Cones and Segre Classes | §4 |

Oct 11 | Renata Picciotto | Deformation to the Normal Cone, Intersection Products | §§5, 6 |

Oct 18 | Reading, Review, Discussion | ||

Oct 25 | Noah Olander | Intersection Multiplicities | §7 |

Nov 1 | Adam Block | Intersections on Nonsingular Varieties | §8 |

Nov 8 | Henry Liu | Excess and Residue Intersections | §9 |

Nov 15 | TBA | Degeneracy Loci and Grassmannians | §14 |

Nov 22 | Thanksgiving - no seminar | ||

Nov 29 | Yakov Kononov | Grothendieck-Riemann-Roch Theorem | §§15,18 |

Dec 6 | Carl Lian | TBA | [L], [M] |

Dec 13 | Carl Lian | TBA | [L], [M] |