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

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