This is an in-house algebra seminar for the Department of Mathematics at Fordham University. We will meet at 1:00 pm on Thursdays at Lincoln Center campus. The current organizer is Han-Bom Moon.
This semester, we will read Ulrich Bundles, written by Costa, Miro-Roig, and Pons-Llopis. The goal is to understand the basic notions of ACM and Ulrich bundles, as well as some known examples. We also explore some interesting questions.
We also read a recent paper:
Anghel, Smooth Counterexamples to the Eisenbud–Schreyer–Weyman Ulrich Existence Problem, arXiv:2609.02718.
Here is a tentative schedule.
Sep. 3. Organization meeting. Sec. 1.1 - 1.3. Vector bundles and Serre's theorem. Speaker: Han-Bom Moon.
Sep. 10. Sec. 1.4 - 1.5. Moduli spaces of vector bundles. Speaker: Alex Scheffelin
Sep. 17. Sec. 2.1. Definition of aCM bundles. Speaker: Valeriy Sergeev
Sep. 24. Sec. 2.2 - 2.4. Examples of aCM bundles. Speaker: Aaron Goodwin
Oct. 1. Sec. 2.5. aCM bundles on hypersurfaces.
Oct. 8. Sec. 3.2. Definition of Ulrich bundles.
Oct. 15. Sec. 3.3 - 3.4. Basic properties and Eisenbud-Schreyer conjecture.
Oct. 22. Sec. 4.1 - 4.2. Ulrich bundles on hypersurfaces.
Oct. 29. Sec. 4.3 - 4.4. Ulrich bundles on general surfaces in P^3.
Nov. 5. Sec. 5.1 - 5.2. Ulrich bundles on surfaces I.
Nov. 12. Sec. 5.3. Ulrich bundles on surfaces II.
Nov. 19. Sec. 5.4 - 5.6. Ulrich bundles on surfaces III.
Nov. 26. Thanksgiving.
Dec. 3. Ch 6. Intersection of quadrics.