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.
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.
|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 [Notes ]|
|Nov 9||Henry Liu||Excess and Residue Intersections||§9|
|Nov 15||Song Yu||Grassmannians, Schubert Calculus||§14|
|Nov 22||Thanksgiving - no seminar|
|Nov 29||Yakov Kononov||Grothendieck-Riemann-Roch Theorem||§§15,18|
|Dec 6||Carl Lian||Intersection Theory on Moduli Spaces of Curves||[L], [M]|
|Dec 14||Carl Lian||Intersection Theory on Moduli Spaces of Curves (cont'd)||[L], [M]|