Algebraic Geometry Seminar

Seminar information archive ~07/21Next seminarFuture seminars 07/22~

Date, time & place Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu

2015/05/18

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Will Donovan (IPMU)
Twists and braids for general 3-fold flops (English)
[ Abstract ]
When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
[ Reference URL ]
http://db.ipmu.jp/member/personal/4007en.html