## 代数幾何学セミナー

開催情報 月曜日　15:30～17:00　数理科学研究科棟(駒場) 122号室 權業 善範・中村 勇哉・高木 俊輔

### 2017年06月12日(月)

17:00-18:30   数理科学研究科棟(駒場) 056号室

Ivan Cheltsov 氏 (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
[ 講演概要 ]
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.