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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2009, Issue 637


Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1

Jun-Muk Hwang
  • Korea Institute for Advanced Study, 207-43 Cheongnyangni-dong, Seoul 130-722, Korea. e-mail:
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Published Online: 2009-11-23 | DOI: https://doi.org/10.1515/CRELLE.2009.095


We show that deformations of a surjective morphism onto a Fano manifold of Picard number 1 are unobstructed and rigid modulo the automorphisms of the target, if the variety of minimal rational tangents of the Fano manifold is non-linear or finite. The condition on the variety of minimal rational tangents holds for practically all known examples of Fano manifolds of Picard number 1, except the projective space. When the variety of minimal rational tangents is non-linear, the proof is based on an earlier result of N. Mok and the author on the birationality of the tangent map. When the varieties of minimal rational tangents of the Fano manifold is finite, the key idea is to factorize the given surjective morphism, after some transformation, through a universal morphism associated to the minimal rational curves.

About the article

Received: 2008-02-11

Revised: 2008-08-06

Published Online: 2009-11-23

Published in Print: 2009-12-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue 637, Pages 193–205, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.095.

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