主 题: Stably Rationality and Diagonal Decomposition
报告人:
时 间: 2016-07-04 08:00 - 2016-07-15 18:00
地 点: 82J12
Topics:
Stably rationality problem, integral Chow and cohomological diagonal decomposition
Organizers:
Zhiyuan Li (Fudan), Zhiyu Tian (CNRS) and Chenyang Xu (BICMR)
Participants:
Qile Chen (Boston College)
Lie Fu (Lyon)
Zhi Jiang (Fudan)
Jun Li (Fudan and Stanford)
Mingmin Shen (Amsterdam)
Xiaowei Wang (Rutgers)
Qizheng Yin (ETH)
Letao Zhang (Stony Brook)
Yi Zhu (Waterloo)
Schedule:
- Warm up: TBA
- rationality: TBA
- Chow Decomposition of Diagonal: TBA
Reference
- Hassett, Some rational cubic fourfolds/ Special cubic fourfolds
- Kollar, Nonrational hypersurface
- Voisin:
Unirational threefolds with no universal codimension $2$ cycle
- Totaro:
Hypersurfaces that are not stably rational
- CT and Pirutka: ?
- Hypersurfaces quartiques de dimension 3: non rationalite stable
- Cyclic covers that are not stably rational
- Beauville:
A very general sextic double solid is not stably rational
- Hassett-Tschinkel:
- Stable rationality and conic bundles
- On stable rationality of Fano threefolds and del Pezzo fibrations
- Hassett-Pirutka-Tschinkel:
- Stable rationality of quadratic surface bundle over surfaces
-
- Cohomological diagonal decomposition
- Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal?
- On the universal $CH_0$ group of cubic hypersurfaces
- Hyperk?hler manifolds of jacobian type
- Rationality, universal generation and the integral Hodge conjecture
Further questions and discussion
- Whether rationality is smooth deformation invariant
- Relation between Chow DDC and cohomological DDC, i.e.
? (i). find an example (dimension is expected >4) which admits cohomological DDC but does not admit Chow DDC
? (ii). find other examples where cohomological DDC is equivalent to Chow DDC
- Possible improvement of Voisin’s criterion
- Stably rationality of conic bundles (threefolds), quadric bundles (fourfolds), cubic fourfolds
