* Pins and needles bend and break, my fair lady...*

In this semester's working CA/AG seminar we will try to read recent papers
of McKernan, Hacon, Birkar, and Cascini where they prove main conjectures of Mori Theory
(except abundance and termination of flips).
The seminar meets on Friday, at 2:35, in LGRT 1634.
The emphasis will be on trying to understand the logic of their proof,
various versions of MMP used in it,
enhance our intuition of Mori Theory,
and look at various applications.

Dates:

Feb 9. Mori cone theorem (Jenia)

Feb 16. Extremal contractions (Jenia)

Feb 23. Flips, flops, log pairs (Jenia)

Mar 2. How to compute discrepancies? (Ana-Maria)

Mar 9. Canonical singularities (Ana-Maria)

Mar 16. Toric Mori Theory (David)

Mar 23. Spring Break.

Mar 30. Toric Mori Theory-2 (David)

Apr 6. Fano Varieties (Evgeny)

Apr 13. No seminar

Apr 20. Mutiplier Ideals (Jessica)

Apr 27. Deformational Invariance of Plurigenera (Jenia)

May 3. On the Minimal Model Program (Paolo Cascini, UCSB). LGRT1634, 4pm.

May 4. Finite generation of the canonical ring
(Paolo Cascini, UCSB)

May 11. Proving termination without proving termination (Jenia)

On May 16 and 17 McKernan (UCSB) and Hacon (Utah) will give talks at the Clay Institute (2pm Hilbert space hall)

Some references and links:

- Existence of minimal models for varieties of log general type,
*McKernan, Hacon, Birkar, and Cascini.*

I have a newer version with less typos - please contact me if you want a copy.

- On the existence of flips,
*Hacon and McKernan*

- Flips and abundance for algebraic threefolds,
*Kollar et al*. I have an extra copy.

This is a technical bible with an exposition of Shokurov's insights about 3-folds.

- Flips for 3-folds and 4-folds,
*Ambro, Corti, Fujino, Hacon, Kollar, McKernan, Takagi*

This is a technical bible with an exposition of Shokurov's insights about 4-folds.

- Birational geometry of algebraic varieties,
*Kollar, Mori*

- Positivity in Algebraic Geometry-I,II,
*Lazarsfeld*, see Sections 9-11 for multiplier ideals and Siu's deformational invariance of plurigenera

- Timeless classic: Higher dimensional complex geometry,
*Clemens, Kollar, Mori*.

- The structure of algebraic threefolds,
*Kollar*

- Analytic approach of Yum-Tong Siu (that we will not pursue):

Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type,

General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring.

Back to Tevelev's homepage