Colloquium

Speaker: Prof. Min Ru (University of Houston)
Title: Holomorphic Curves into Algebraic Varieties
Time: 2008-07-03 (Thu.)  15:00 - 16:00
Place:
Abstract: In 1933, H. Cartan obtained the defect relation for linearly nondegenerate holomorphic mappings into the complex project space intersecting hypeprlanes. In this talk, I'll discuss how to extend it to algebraic nondegenerate holomorphic mappings into an arbitrary non-singular complex projective variety $V$, as well as intersecting possible non-linear hypersurfaces. Our method consists of embedding $V$ into a linear variety by means of a suitable Veronese map and then apply Cartan's defect relation. In doing so, we first derive, for a projective variety $X$, an explicit lower bound of the $m$-th normalized Hilbert weight of $X$ in terms of the normalized Chow weight of $X$ (or Mumford's degree of contact).
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