COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Igusa quartic and and Wiman-Edge sextics

## Igusa quartic and and Wiman-Edge sexticsAdd to your list(s) Download to your calendar using vCal - Ivan Cheltsov (Edinburgh)
- Wednesday 10 May 2017, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Caucher Birkar. The automorphism group of Igusa quartic is the symmetric group of degree 6. There are other quartic threefolds that admit a faithful action of this group. One of them is the famous Burkhardt quartic threefold. Together they form a pencil that contains all $\mathfrak{S}_6$-symmetric quartic threefolds. Arnaud Beauville proved that all but four of them are irrational, while Burkhardt and Igusa quartic are known to be rational. Cheltsov and Shramov proved that the remaining two threefolds in this pencil are also rational. In this talk, I will give an alternative prove of both these (irrationality and rationality) results. To do this, I will describe Q-factorizations of the double cover of the four-dimensional projective space branched over the Igusa quartic, which is known as Coble fourfold. Using this, I will show that $\mathfrak{S}_6$-symmetric quartic threefolds are birational to conic bundles over the quintic del Pezzo surface whose degeneration curves are contained in the pencil studied by Wiman and Edge. This is a joint work with Sasha Kuznetsov and Costya Shramov from Moscow. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- CMS MR13
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsEconomic orthodoxy and barriers to the low-carbon economy Type the title of a new list here Hinsley Lecture Series## Other talksCambridge-Lausanne Workshop 2018 - Day 2 Recent Advances in Solid State Batteries and Beyond Li Technologies - Challenges for Fundamental Science Introduction to early detection and tumour development On the origin of human sociality: Ape minds and the evolution of Homo sapiens Emergence in Physics: Life, the Universe and the Nature of Reality |