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Geometry of minimal rational curves on Fano manifolds

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Abstract

This lecture is an introduction to my joint project with N. Mok where we develop a geometric theory of Fano manifolds of Picard number 1 by studying the collection of tangent directions of minimal rational curves through a generic point. After a sketch of some historical background, the fundamental object of this project, the variety of minimal rational tangents, is defined and various examples are examined. Then some results on the variety of minimal rational tangents are discussed including an extension theorem for holomorphic maps preserving the geometric structure. Some applications of this theory to the stability of the tangent bundles and the rigidity of generically finite morphisms are given. (author)
Authors:
Hwang, J -M [1] 
  1. Korea Institute for Advanced Study, Seoul (Korea, Republic of)
Publication Date:
Dec 15, 2001
Product Type:
Conference
Report Number:
INIS-XA-857; LNS-016006
Resource Relation:
Conference: School on vanishing theorems and effective results in algebraic geometry, Trieste (Italy), 25 Apr - 12 May 2000; Other Information: 46 refs, 2 tabs; Related Information: In: Vanishing theorems and effective results in algebraic geometry, ICTP lecture notes CD seriesv. 6, by Demailly, J.P. [Universite de Grenoble (France)]; Goettsche, L. [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]; Lazarsfeld, R. [University of Michigan (United States)] (eds.), 397 pages.
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; FUNCTIONS; GEOMETRY; LECTURES; MAPS; MATHEMATICAL MANIFOLDS; STABILITY; TOPOLOGY
OSTI ID:
20854864
Research Organizations:
Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISBN 92-95003-09-8; TRN: XA0600674027884
Availability:
Available from INIS in electronic form; Also available on-line: http://www.ictp.it
Submitting Site:
INIS
Size:
page(s) 335-394
Announcement Date:
Apr 23, 2007

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Citation Formats

Hwang, J -M. Geometry of minimal rational curves on Fano manifolds. IAEA: N. p., 2001. Web.
Hwang, J -M. Geometry of minimal rational curves on Fano manifolds. IAEA.
Hwang, J -M. 2001. "Geometry of minimal rational curves on Fano manifolds." IAEA.
@misc{etde_20854864,
title = {Geometry of minimal rational curves on Fano manifolds}
 author = {Hwang, J -M}
 abstractNote = {This lecture is an introduction to my joint project with N. Mok where we develop a geometric theory of Fano manifolds of Picard number 1 by studying the collection of tangent directions of minimal rational curves through a generic point. After a sketch of some historical background, the fundamental object of this project, the variety of minimal rational tangents, is defined and various examples are examined. Then some results on the variety of minimal rational tangents are discussed including an extension theorem for holomorphic maps preserving the geometric structure. Some applications of this theory to the stability of the tangent bundles and the rigidity of generically finite morphisms are given. (author)}
 place = {IAEA}
 year = {2001}
 month = {Dec}
 }