Algebraic Geometry Seminar

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

2013/01/15

15:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jungkai Alfred Chen (National Taiwan University)
Three Dimensional Birational Geoemtry--updates and problems (ENGLISH)
[ Abstract ]
In this talk I will talk about some recent results on
biratioanl classification and biratioanl geoemtry of threefolds.

Given a threefold of general type, we improved our previous result by
showing that $Vol \\ge 1/1680$ and $|mK_X|$ is biratioanl for $m \\ge
61$.
Compare with the worst known example that $X_{46} \\subset
\\mathbb{P}(4,5,6,7,23)$, one also knows that there are only finiteley
many singularities type
for threefolds of general type with $1/1680 \\le Vol \\le 1/420$. It is
then intereting to study threefolds of general type with given basket
of singularities and with given fiber structure.
Concerning threefolds with intermediate Kodaira dimension, we
considered the effective Iitaka fibration. For this purpose, it is
interesting to study threefolds with $\\kappa=1$ with given basket of
singularities and abelian fibration.

For explicit birational geoemtry, we will show our result that each
biratioanl map in minimal model program can be factored into a
sequence of following maps (or its inverse)
1. a divisorial contraction to a point of index r with discrepancy 1/r.
2. a blowup along a smooth curve
3. a flop