This is an in house algebra seminar for department of mathematics at Fordham University. We will meet at 1:30 pm on Thursdays, at Lincoln Center campus. The current organizer is Han-Bom Moon.
This year, we will read Debarre, Higher Dimensional Algebraic Geometry. The goal is to understand basic notions of birational algebraic geometry on complex projective algebraic varieties, and prepare ourselves in more advanced topics including Mori dream spaces and moduli spaces of higher dimensional varieties.
The following books are good references.
Kollár, Rational curves on algebraic varieties.
Kollár, Mori, Birational geometry of algebraic varieties.
Lazarsfeld, Positivity in algebraic geometry.
Here is a tentative schedule.
Sep. 4. Organization meeting. Sec. 1.1 - 1.2, Intersection numbers. Speaker: Han-Bom Moon. Notes
Sep. 11. Sec. 1.3 - 1.5, Cone of curves and ample divisors. Speaker: Connor Stewart
Sep. 18. Sec. 1.6 - 1.8, Nef divisors and Kleiman criterion. Speaker: Valeriy Sergeev
Sep. 25. Sec. 1.9 - 1.11, Exceptional locus. Speaker: Connor Stewart
Oct. 2. No seminar.
Oct. 9. Sec. 2.1 - 2.2, Parametrizing morphisms I. Speaker: Sevan Bharatan
Oct. 16. Sec. 2.3 - 2.4, Parametrizing morphisms II. Speaker: Han-Bom Moon
Oct. 23. Sec. 3.1 - 3.3, Bend-and-break I. Speaker: Aaron Goodwin
Oct. 30. Sec. 3.4 - 3.5, Bend-and-break II. Speaker: Alex Scheffelin
Nov. 6. Sec. 3.6 - 3.9, Bend-and-break III.
Nov. 13. No seminar.
Nov. 20. Sec. 4.1 - 4.3. Uniruled and rationally connected varieties I.
Nov. 27. No seminar. Thanksgiving.
Dec. 4. Sec. 4.1 - 4.3. Uniruled and rationally connected varieties II.