Seminar on Complex
Analysis and Complex Geometry - Spring 2010
All talks in 646A PGH,
Wednesday, 12:00-1:00 PM
Friday (!!!), April 30, 2010
Title: A codimension two CR singular submanifold
Speaker: Xiaojun Huang, Rutgers University
Abstract: Let $M\subset \mathbb{C}^{n+1}$ ($n\geq 2$) be a real analytic submanifold
defined by an equation of the form: $w=|z|^2+O(|z|^3)$, where we use
$(z,w)\in \mathbb{C}^{n}\times \mathbb{C}$ for the coordinates of
$\mathbb{C}^{n+1}$. We first derive a pseudo-normal form for $M$ near 0.
We then use it to prove that $(M,0)$ is holomorphically equivalent to the
quadric $(M_\infty: w=|z|^2,0)$ if and only if it can be formally
transformed to $(M_\infty,0)$. We also use it to give a necessary and
sufficient condition when $(M,0)$ can be formally flattened. The result is
due to Moser for the case of $n=1$.
Wednesday, March 24, 2010
Title: Curvature and complex structures
Speaker: Bun Wong, UC Riverside
Abstract: In this talk we will report on some progresses of two open
problems regarding Kahler manifolds with positive or negative holomorphic
sectional curvature. In the negative case (joint with Gordon Heier and
Steven Lu) we will discuss a possible proof of the Lang/Kobayashi conjecture
that the canonical system of a compact Kahler manifold with negative
holomorphic sectional curvature is ample. In the positive case (joint work
with Gordon Heier), we will explore a problem of S.T. Yau about the
unirationality of compact Kahler manifolds with positive holomorphic
sectional curvature.
Wednesday, March 10, 2010
Title: Complex Geometry Group working seminar
Speaker: Gordon Heier, University of Houston
Abstract: Current topics from the Complex Geometry Group will be discussed.
Wednesday, March 03, 2010
Title: Complex Geometry Group working seminar
Speaker: Gordon Heier, University of Houston
Abstract: Current topics from the Complex Geometry Group will be discussed.
Wednesday, February 17, 2010
Title: Non-integrated defect relation for meromorphic maps of complete Kahler manifold intersecting hyper surfaces in projective space II
Speaker: Suraizou Sogome, University of Houston
Abstract: We give a non-integrated defect for a meromorphic map of a complete
K$\ddot{a}$hler manifold whose universal covering is biholomorphic to the ball in
$\mathbb{C}^m$ into $\mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general
position and an application of this non-integrated defect to the Gauss map of a closed
regular submanifold of $\mathbb{C}^m$.
The result provides a complement to the recent result of Ru on the defect relation for
meromorphic mappings from
$\mathbb{C}^m$ into $\mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general
position.\\
This is a joint work with Dr Ru.
Wednesday, February 10, 2010
Title: Non-integrated defect relation for meromorphic maps of complete Kahler manifold intersecting hyper surfaces in projective space
Speaker: Suraizou Sogome, University of Houston
Abstract: We give a non-integrated defect for a meromorphic map of a complete
K$\ddot{a}$hler manifold whose universal covering is biholomorphic to the ball in
$\mathbb{C}^m$ into $\mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general
position and an application of this non-integrated defect to the Gauss map of a closed
regular submanifold of $\mathbb{C}^m$.
The result provides a complement to the recent result of Ru on the defect relation for
meromorphic mappings from
$\mathbb{C}^m$ into $\mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general
position.\\
This is a joint work with Dr Ru.
Wednesday, February 3, 2010
Title: Birational geometry of holomorphic symplectic varieties.
Speaker: Brendan Hassett, Rice University
Abstract: We propose a general framework governing the intersection properties of
extremal rays of irreducible holomorphic symplectic manifolds.
Our main thesis is that extremal rays associated to Lagrangian projective
subspaces control the behavior of the cone of curves. We explore
implications of this philosophy for examples like Hilbert schemes of
points on K3 surfaces and generalized Kummer varieties. We also present
evidence supporting our conjectures in specific cases.
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