複素幾何セミナーの記録

１月１８日（水）１５：００〜１８：００（時間がいつもと違います）

修士論文発表会の練習（順不同）

山本桃果（首都大学東京）　ある楕円曲面のMordell-Weil群の生成元とその応用
大枝真之（首都大学東京）　Hodge filtrationとpole order filtrationの関係性
片倉雄輝（首都大学東京）　トロピカル曲線上の線形系と有理写像について
新庄みずほ（首都大学東京）　種数3の非特異トロピカル曲線のゴナリティ
二宮尚人（首都大学東京）　2次元のヤコビアン予想について
西野哲（首都大学東京）　トロピカル射影平面上の線形力学系
玉置昂（首都大学東京）　関数体上の楕円曲線の 3 等分点を用いたガロア表現とある平面曲線について
小鳥圭介（首都大学東京）　A_3不変多項式のなす部分空間のイニシャルベクトル空間の個数とオイラー関数


１１月３０日（水）１５：００〜１８：００（時間がいつもと違います）
修士論文中間発表会


１０月２５日（火）１４：００〜１５：００（時間がいつもと違います）

Alan Huckleberry氏（Ruhr大学，Bochum）

On complex geometric curvature of flag domains

Abstract:
Flag domains are complex manifolds which arise as open orbits of real Lie groups in flag manifolds of their
complexifications. They play an important role in the theory of parameter spaces of complex structures on
compact algebraic manifolds (period domains, Hodge theory, Mumford-Tate domains) and in the representation
theory of semisimple Lie groups.In the lecture we will discuss flag domains from the complex analytic viewpoint,
in particular discussing their Levi curvature. Classical results which use their intrinsic Hermitian geometry,
and which yield strong statements about the degree of positivity of the Levi form, will be outlined. Recent
results of the speaker and his co-authors which contribute to understanding the negative curvature
(pseudoconcavity) will be presented. While the results on the positive side lead to vanishing of cohomology
in high degree, results on pseudoconcavity can be applied in the low range and thereby lead to information about
the function-theoretic phenomena of these domains.


４月２７日（水）１６：３０〜１７：３０

Isac Heden氏（京都大学数理解析研究所）

Extensions of principal additive bundles over a punctured surface.

Abstract: We study complex affine G_a-threefolds X such that the
restriction of the quotient morphism \pi\colon X\to S to \pi^{-1}(S_*)
is a principal G_a-bundle, where S_* denotes the complement of a
closed point in S. Changing the point of view, we look for affine
extensions of G_a-principal bundles over punctured surfaces, i.e
affine varieties that are obtained by adding an extra fiber to the
bundle projection over the puncture. The variety SL_2 will be of
special interest and a source of many examples.