## 代数幾何学セミナー

開催情報 火曜日　10:30～11:30 or 12:00　数理科学研究科棟(駒場) ハイブリッド開催/002号室 權業 善範・中村 勇哉・田中公

### 2007年06月22日(金)

16:30-18:00   数理科学研究科棟(駒場) 118号室
Qi Zhang 氏 (Missouri大学)
Projective varieties with nef anti-canonical divisors
[ 講演概要 ]
Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.

### 2007年05月15日(火)

14:30-16:00   数理科学研究科棟(駒場) 122号室
いつもと時間・曜日・場所が異なります。
Mikhail Kapranov 氏 (Yale 大学)
Riemann-Roch for determinantal gerbes and smooth manifolds
[ 講演概要 ]
A version of the Riemann-Roch theorem for curves due to Deligne, describes the determinant of the cohomology of a vector bundle E on a curve.
If one realizes E via the Krichever construction, the determinant of the cohomology becomes a Hom-space in the determinantal gerbe for the vector space over the field of power series. So one has a local" Riemann-Roch problem of description of this gerbe itself. The talk will present the results of a joint work with E. Vasserot describing the class of such a gerbe in a family which geometrically can be seen as a circle fibration. This can be further generalized to the case of a fibration with fibers being smooth compact manifolds of any dimension d (joint work with P. Bressler, B. Tsygan and E. Vasserot).

### 2007年05月07日(月)

16:30-18:00   数理科学研究科棟(駒場) 122号室

Pathologies on ruled surfaces in positive characteristic
[ 講演概要 ]
We discuss some pathologies of log varieties in positive characteristic. Mainly, we show that on ruled surfaces there are counterexamples of several logarithmic type theorems. On the other hand, we also give a characterization of the counterexamples of the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface by means of the Tango invariant of the base curve.

### 2007年03月26日(月)

15:30-17:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
Existence of minimal models and flips (3rd talk of three)

### 2007年03月22日(木)

10:30-12:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
On boundedness of log Fano varieties (2nd talk of three)

### 2007年03月20日(火)

16:30-18:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge
)
Singularities and termination of flips (1st talk of three)

### 2007年01月26日(金)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Professor Frans Oort
(Department of Mathematics
University of Utrecht
)
Irreducibility of strata and leaves in the moduli space of
abelian varieties I (a survey of results)

### 2006年12月08日(金)

15:00-16:25   数理科学研究科棟(駒場) 126号室
Stefan Kebekus 氏 氏 (Mathematisches Institut
Universität zu Köln
)
Rationally connected
foliations

### 2006年12月04日(月)

16:30-18:00   数理科学研究科棟(駒場) 126号室
Professor Burt Totaro

(University of Cambridge)

When does a curve move on a surface, especially over a finite field?

### 2006年11月13日(月)

16:30-18:00   数理科学研究科棟(駒場) 126号室

Hom stacks and Picard stacks

### 2006年10月18日(水)

16:00-18:15   数理科学研究科棟(駒場) 122号室
E. Esteves 氏 (IMPA) 16:00-17:00

Jets of singular foliations and applications
to curves and their moduli spaces

F. Zak 氏 (Independent Univ. of Moscow) 17:15-18:15
Dual varieties, ramification, and Betti numbers
of projective varieties