Monthly Archives: October 2017

Algebraic geometry session at AMS Fall Sectional Meeting @ UC Riverside, 4–5 November 2017

I’ll be speaking (on rationality) at the AMS Fall Sectional Meeting at Riverside. Other speakers in the algebraic geometry session are Aravind Asok, Emily Clader, Omprokash Das, Humberto Diaz, Matthias Flach, Martin Gallauer, James McKernan, Wenhao Ou, Dustin Ross, and Alexander Soibelman. The session is organized by Humberto Diaz, Jose Gonzalez, and Ziv Ran.

The invited addresses are by Paul Balmer, Pavel Etingof, and Monica Vazirani.

Photo: NO YOU CAN’T HAVE MY LEAVES STOP ASKING, from reddit.

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New paper: The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay

I’ve posted a new paper on the arXiv. Most of the results premiered at Oberwolfach, but since then I’ve added an interesting new example inspired by related work of Takehiko Yasuda, whom I met there. (Oberwolfach at work!)

The paper shows that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0. Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.

Image: Palmerston, Foreign Office cat, sneaks up on cheese; from his DiploMog twitter feed

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