Seminars
2025 NCKU algebraic geometry student seminar
Venue: Department of Mathematics, NCKU.
Date: 2025 June - August.
- 6/09 11:00-13:00 Ching-Jui Lai (NCKU), Birational geometry of complex projective surfaces, a brief introduction Link
- 6/26 10:00-12:00 Sheng-Chun Tsai (NCKU), Introduction to vector bundles, Cartier divisor, and linear systems.
- 7/04 10:00-12:00 Li-Chen Liu (NCKU), Bezout’s theorem in projective spaces.
Aim and Scope:
This seminar aims to train participants fundamentals in algebraic geometry to prepare for future research. We plan to cover basic tools and rudiments in algebraic geometry by working through standard textbooks, at times bringing in outside material in the forms of more advanced textbook material.
We shall begin with the following topics.
- Sheaves and sheaf cohomology (via Cech cohomology) [H, II.1, III.4-III.5]
- Languange of schemes [H, II.2-II.4]
- Divisors, line bundles, linear systems [H, II.5-II.7]
If time permits, we will also discuss some advanced topics. The tentative targets might include
- Cohomological criterion for affineness of schemes [H, III.3]
- Canonical systems of non-singular complete curves [H, VI]
- Castelnuovo’s contraction theorem and strong factorization [B]
- Intersection theory (via asymptotic Riemann–Roch) [K, Appendix]
- Moduli functors and Hilbert schemes [FAG]
We plan to hold the first meeting in mid-June.
References
- [H] Algebraic Geometry, R. Hartshorne
- [B] Complex algebraic surfaces, A. Beauville
- [K] Rational curves on algebraic varieties, J. Kollár
- [FAG] Fundamental algebraic geometry: Grothendieck’s FGA explained, B. Fantechi et al.
Organizers
- Ching-Jui Lai (NCKU)
- Tsung-Ju Lee (NCKU)