## セミナー -- Algebraic Geometry Seminar

Title

**
A geometric characterisation of Arithmetic surfaces
**

Date

April 27, 2009, 13:00--

Room

Room 115, RIMS, Kyoto University

Speaker

Kapil Hari Paranjape (Inst. Math. Sci., Chennai, India)

Abstract
A result of Belyi can be stated as follows. Every curve
defined over a number field can be expressed as a cover of the
projective line with branch locus contained in a rigid divisor. We
define the notion of geometrically rigid divisors in surfaces and then
show that every surface defined over a number field can be expressed as
a cover of the projective plane with branch locus contained in a
geometrically rigid divisor in the plane. The main result is the
characterisation of arithmetically defined divisors in the plane as
geometrically rigid divisors in the plane.

Organizer
S. Mukai

Title

**
Non-commutative Mori contractions
**

Date

April 16, 2009, 14:00--

Room

Room 202, RIMS, Kyoto University

Speaker

Daniel Chan (University of New South Wales, Australia)

Abstract
There is a conjecture of Mike Artin's which can be
loosely stated as "non-commutative surfaces are, up to
birational equivalence, either ruled or finite over their
centre". One problem with tackling this question is the
lack of methods for constructing morphisms in non-commutative
algebraic geometry. In this talk I will introduce some of the
basics of non-commutative algebraic geometry and give a method
for constructing morphisms from a non-commutative scheme to a
commutative curve. This is used to give analogues of the Mori
contraction of a K-negative curve with self-intersection zero
on a smooth projective surface.

Organizer
S. Mukai

Title

**
Inductive algorithm of resolution of singularities by Encinas and Villamayor**

Date

February 14 , 2002, 14:00--

Room

Room 402, RIMS, Kyoto University

Speaker

松木 謙二 （パーデュー大学）

Comments

Organizers
S. Mori, N. Nakayama