Chennai Mathematical Institute

Dr. F.C. Kohli Centre of Excellence


Sándor Kovács, December 2023

Professor Sándor Kovács of University of Washington, Seattle will visit CMI in December, 2023. He will give 6 lectures titled Introduction to the moduli theory of higher dimensional varieties. The details of the talks are given below:

Schedule : 

7th December 2023, 15:30-16:30 
8th December 2023, 15:30-16:30 
11th December 2023, 15:30-16:30 
12th December 2023, 15:30-16:30 
13th December 2023, 10:30-11:30 
13th December 2023, 15:30-16:30

Topics

  1. Overview and some history of moduli theory, statements of the main results
  2. Comparison to M_g. Why is this a lot harder? (difficulties, obstacles, long time roadblocks)
  3. Stable and related singularities and their deformations
  4. Moduli theory without a boundary
  5. Moduli of pairs I: flat divisorial part, ``large'' coefficients
  6. Moduli of pairs II: K-flatness, marked pairs.

Audience will be expected to be familiar with the following topics: basic algebraic geometry (first three chapters of Hartshorne).

It would be useful to be familiar with the topics covered in the NCM programme on birational geometry held at CMI during May 22 - June 3, 2023.

Some of the more advanced preparatory material will be discussed in a series of online lectures.

References

  1. Kovács, Young person's guide to moduli theory
  2. Hacon and Kovács, Classification of Higher Dimensional Algebraic Varieties https://link.springer.com/book/10.1007/978-3-0346-0290-7
  3. Kollár, Families of Varieties of General Type
  4. Kovács, Singularities of stable varieties, Handbook of moduli. Vol. II, Adv. Lect. Math. (ALM), vol. 25, Int. Press, Somerville, MA, 2013, pp. 159203 https://arxiv.org/abs/1102.1240
  5. Kovács, Moduli of stable log-varieties -- an update. Algebraic geometry: Salt Lake City 2015, 403417. Proc. Sympos. Pure Math.,97.1 American Mathematical Society, Providence, RI, 2018 (available at https://www.ams.org/books/pspum/097.1/)

Schedule for the preparatory lectures

  1. V. Balaji: Moduli, 11th November 2023, 10:30.
  2. Omprokash Das: Minimal model program and its singularities, 13th and 15th November 2023, 11:00. Notes: Part 1 and Part 2.
  3. Manoj Kummini: Non-normal schemes, 16th and 18th November 2023, 15:30. Notes: Part 1 and Part 2.
  4. Sandor Kovacs: Families of varieties of general type, date : 20th November 2023, 10:00. Notes.