講演者

Ivan Cheltsov氏（Univeristy of Edinburgh）

タイトル

Rationality of two Fano threefolds.

アブストラクト

Burkhardt and Igusa quartic threefolds are classically known to be rational. They generate a pencil of quartics that all admit an action of the symmetric group of degree six. Bondal and Prokhorov asked which threefolds in this pencil are rational and which are not. All these threefolds are singular, so Iskovskikh and Manin’s result cannot be applied here. Beauiville proved that every quartic threefold in this pencil is irrational except for Burkhardt and Igusa quartics and possibly two more threefolds. In this talk I will show how to use two constructions of Todd (dated back to 1933 and 1935) to prove that the remaining two quartic threefolds in the pencil are also rational. Then I will give an alternative approach to Beauville’s theorem. This is a joint work with Costya Shramov from Moscow.

連続講義：なお6/5から6/9までCheltsov氏による集中講義があります。
場所：埼玉大学理学部1号館3階　基礎数理演習室