Notes for the course on the Minimal Model Program I'm giving with Michael Temkin as part of the Kazhdan Sunday Seminars, Winter 2023-23. I will update them after each lecture. Last updated: Jan. 27, 2024.
Notes from 2012 VIGRE Summer School in Algebraic Geometry at UGA: Please note that these are a rough draft and were live-TEX-ed, so they contain both mistakes and at times poor typesetting.
Lines on a cubic surface. These are notes on how to use Chern classes to calculate the number of lines on a cubic surface.
Notes from studying for my oral qual exam. These include a very detailed exposition of the first 7 chapters of Fulton's book on Intersection Theory, including the details of many of his "examples". It also includes some notes on complex algebraic surfaces, including ADE singularity classification and details about K3 and Enriques surfaces. For those preparing for their own oral quals, here was my syllabus.
Notes from my talk on Kontsevich's formula for the number of rational plane curves of degree d passing through 3d-1 general points. This talk was given at the Graduate Student Pizza Seminar on Friday, Sept. 14, 2012. My reference, and a great place to actually learn the technical details behind the talk, is Kock and Vainsencher's book "An Invitation to Quantum Cohomology." My notes and talk were intended for an audience without any background in algebraic geometry.
Notes from my talk on how to construct a toric variety from a fan, and how the local properties of that toric variety follow directly from the cones in the fan. This was the second talk in the Grad Student AG seminar, Fall 2012.
Notes from my talk on criteria for determining when a Cartier divisor is base-point free or ample. Also covers formula for dimension of global sections and an application to the Toric Chow Lemma. This was the talk in the Grad Student AG Seminar,11/14/2012.
Notes I'm currently writing up the background needed to understand the construction and basic properties of the moduli space of curves as well as Konstevich's moduli space of stable maps. These notes can be seen as a companion to the fundamental papers of Deligne-Mumford, and the notes of Fulton-Pandharipande and Dan Edidin on these topics.
Notes from my talk in the Grad Student AG Seminar, Nov. 28, 2012 on toric intersection theory.
Finite group quotients and Dual Abelian Varieties : notes from the GSAG Seminar, Feb. 28, 2013.