## Algebraic Geometry Seminar

Seminar information archive ～02/27｜Next seminar｜Future seminars 02/28～

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.) |
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Organizer(s) | GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu |

**Seminar information archive**

### 2007/06/22

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Projective varieties with nef anti-canonical divisors

**Qi Zhang**(Missouri大学)Projective varieties with nef anti-canonical divisors

[ Abstract ]

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.

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.

### 2007/05/15

14:30-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Riemann-Roch for determinantal gerbes and smooth manifolds

**Mikhail Kapranov**(Yale 大学)Riemann-Roch for determinantal gerbes and smooth manifolds

[ Abstract ]

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).

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).

### 2007/05/07

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Pathologies on ruled surfaces in positive characteristic

**謝啓鴻(Xie Qihong)**(東大・数理)Pathologies on ruled surfaces in positive characteristic

[ Abstract ]

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.

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.

### 2007/03/26

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Existence of minimal models and flips (3rd talk of three)

**Professor Caucher Birkar**(University of Cambridge)Existence of minimal models and flips (3rd talk of three)

### 2007/03/22

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On boundedness of log Fano varieties (2nd talk of three)

**Professor Caucher Birkar**(University of Cambridge)On boundedness of log Fano varieties (2nd talk of three)

### 2007/03/20

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

)

Singularities and termination of flips (1st talk of three)

**Professor Caucher Birkar**(University of Cambridge)

Singularities and termination of flips (1st talk of three)

### 2007/01/26

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

University of Utrecht

)

Irreducibility of strata and leaves in the moduli space of

abelian varieties I (a survey of results)

**Professor Frans Oort**

(Department of MathematicsUniversity of Utrecht

)

Irreducibility of strata and leaves in the moduli space of

abelian varieties I (a survey of results)

### 2006/12/08

15:00-16:25 Room #126 (Graduate School of Math. Sci. Bldg.)

Universität zu Köln

)

Rationally connected

foliations

**Stefan Kebekus 氏**(Mathematisches InstitutUniversität zu Köln

)

Rationally connected

foliations

### 2006/12/04

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

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

**Professor Burt Totaro**

(University of Cambridge)When does a curve move on a surface, especially over a finite field?

### 2006/11/13

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Hom stacks and Picard stacks

**青木昌雄**(京大数理研)Hom stacks and Picard stacks

### 2006/10/18

16:00-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Jets of singular foliations and applications

to curves and their moduli spaces

Dual varieties, ramification, and Betti numbers

of projective varieties

**E. Esteves**(IMPA) 16:00-17:00Jets of singular foliations and applications

to curves and their moduli spaces

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

of projective varieties