Time/Location: MWF: 1:28-2:21, Central Classroom Building 0326
Instructor: Hsian-Hua Tseng
Office: 642 Math Tower
Office Phone: 614-292-5581
E-mail: hhtseng-at-math-dot-ohio-state-dot-edu
Office Hours: TBA, or by appointment.
TA: None
Textbook: "Algebraic Geometry'', by Robin Hartshorne (published by Springer-Verlag).
Description: This is the second course, in a three-quarter sequence, of graduate-level algebraic geometry. The goal of the sequence is to discuss the foundational materials of algebraic geometry, in order to prepare graduate students for further study and research in algebraic geometry and related fields. The combined plan for Math 841 and 842 (to be offered in the spring) is to cover Chapters 2 and 3 of the text.
Grading: Based on Homeworks.
Homework Assignments:
updated periodically.
Homework 1 (due Jan. 15):
Ch II Ex. 1.8, 1.16, 1.17.
Homework 2 (due Feb. 01):
Ch II Ex. 2.3, 2.4, 2.6, 2.11, 2.19, and
1. Let $X$ be a scheme. Let $U, V$ be open affines in $X$, and let $\phi: U\to Sepc A$, $\psi: V\to Spec B$ be isomorphisms of schemes. Show that for any $p\in U\cap V$ there is an open subset $W\subset U\cap V$ and $f\in A, g\in B$ such that $p\in W$ and $\phi(W)=D(f), \phi(W)=D(g)$.
Homework 3 (due Feb. 08):
Ch II Ex. 3.2, 3.3, 3.5, 3.6, 3.8.
Homework 4 (due Feb. 15):
Ch II Ex. 3.11, 3.15, 4.2, 4.8, and
1. Prove directly (without using the fact that projective morphisms are proper) that the natural map $\mathbb{P}^n_A\to Spec A$ is closed.
Homework 5 (due Mar. 12):
Ch II Ex. 5.1, 5.2, 5.3, 5.7, 5.9, 5.10, 5.13.