Algebraic Curves in January

Algebraic curves in projective space have a long history, blending the classical geometry of the nineteenth century with modern tools from scheme theory and moduli spaces. This lecture series will examine practical aspects of curves in projective space, emphasizing examples in low genus. We will follow excerpts from Eisenbud and Harris's recent textbook, The Practice of Algebraic Curves. See here for errata.

The lectures will be given by Nathan Pflueger, supported by Bernd Sturmfels.

SCHEDULE

07.01.2026, 14:00-16:00 Linear series §1 & Rational functions and plane curves §2 (Nathan Pflueger)

07.01.2026, 16:00-18:00 Exercises (led by Bernd Sturmfels)

08.01.2026, 10:00-12:00 Rational curves (Lakshmi Ramesh) §3 Newton polygons (Vincenzo Galgano and Jessica Alessandri)

08.01.2026, 14:00-16:00 Canonical curves §2 & Low-genus curves§4,6,9 (Nathan Pflueger)

12.01.2026, 10:00-11:30 Catching Up (led by Smita Rajan & Bernd Sturmfels)

12.01.2026, 14:00-16:00 Hilbert schemes §7 & Hurwitz spaces and Severi varieties §8.5-6 (Nathan Pflueger)

12.01.2026, 16:00-18:00 Exercises (led by Bernd Sturmfels)

13.01.2026, 10:00-12:00 The moduli space (Dmitrii Pavlov) & Intersection theory on moduli spaces (Smita Rajan)

13.01.2026, 14:00-16:00 Curves on scrolls §17 & Castelnuovo's theorem §10 (Nathan Pflueger)

14.01.2026, 14:00-16:00 Brill--Noether theory §12 & Brill--Noether varieties (Nathan Pflueger)

14.01.2026, 16:00-18:00 Exercises (led by Bernd Sturmfels)

19.01.2026, 9:00-11:00 Moduli of stable maps (Felix Lotter and Carl Waller) & Curves in Macaulay2 (Alejandro Ovalle and Svala Sverrisdottir)

19.01.2026, 11:00-12:00 Discussions (led by Bernd Sturmfels)

19.01.2026, 14:00-16:00 Inflection points §13 & The interpolation theorem (Theorem 12.11) (Nathan Pflueger)

Date and time info
07.01.2026: 14:00-18:00, 08.01.2026: 10:00-12:00 + 14:00-16:00, 12.01.2026: 10:00-11:30, 14:00-18:00, 13.01.2026: 10:12:00 + 14:00-16:00, 14.01.2026: 14:00-18:00, 19.01.2026: 9:00-12:00 + 14:00-16:00