## Algebraic Geometry Seminar

Seminar information archive ～03/03｜Next seminar｜Future seminars 03/04～

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 |

### 2017/05/30

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Contractible affine threefolds in smooth Fano threefolds (English or Japanese)

**Masaru Nagaoka**(The University of Tokyo)Contractible affine threefolds in smooth Fano threefolds (English or Japanese)

[ Abstract ]

By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.

Schneider, it is completed to classify all projective compactifications

of the affine $3$-space $\mathbb{A}^3$ with Picard number one.

As a similar question, T. Kishimoto raised the problem to classify all

triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds

$V$ of Picard number two, contractible affine threefolds $U$ as open

subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.

He also solved this problem when the log canonical divisors $K_V+D_1+D_2

$ are not nef.

In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose

log canonical divisors are linearly equivalent to zero.

I will also explain how to determine all Fano threefolds $V$ which

appear in such triplets.

By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.

Schneider, it is completed to classify all projective compactifications

of the affine $3$-space $\mathbb{A}^3$ with Picard number one.

As a similar question, T. Kishimoto raised the problem to classify all

triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds

$V$ of Picard number two, contractible affine threefolds $U$ as open

subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.

He also solved this problem when the log canonical divisors $K_V+D_1+D_2

$ are not nef.

In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose

log canonical divisors are linearly equivalent to zero.

I will also explain how to determine all Fano threefolds $V$ which

appear in such triplets.