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Seminar on Geometric Complex Analysis
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2006/05/22
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)
[ Abstract ]
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.
