Algebraic Geometry Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

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

2018/11/27

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Nobuo Hara (Tokyo University of Agriculture and Technology)
Frobenius summands and the finite F-representation type (TBA)
[ Abstract ]
We are motivated by a question arising from commutative algebra, asking what kind of
graded rings in positive characteristic p have finite F-representation type. In geometric
setting, this is related to the problem to looking out for Frobenius summands. Namely,
given aline bundle L on a projective variety X, we want to know how many and what
kind of indecomposable direct summands appear in the direct sum decomposition of
the iterated Frobenius push-forwards of L. We will consider the problem in the following
two cases, although the present situation in (2) is far from satisfactory.
 (1) two-dimensional normal graded rings (a joint work with Ryo Ohkawa)
 (2) the anti-canonical ring of a quintic del Pezzo surface