Boundary singularities of biholomorphic maps

AbstractIn this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ⋊ Aut σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut σ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Aut σ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.

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Biholomorphic maps of weakly pseudoconvex domains

Duke Mathematical Journal ◽

10.1215/s0012-7094-78-04533-7 ◽

1978 ◽

Vol 45 (4) ◽

pp. 711-719 ◽

Cited By ~ 23

Author(s):

Eric Bedford ◽

John Erik Forn�ss

Keyword(s):

Pseudoconvex Domains ◽

Weakly Pseudoconvex ◽

Biholomorphic Maps

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The closing lemma for holomorphic maps

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385797086227 ◽

1997 ◽

Vol 17 (4) ◽

pp. 821-837 ◽

Cited By ~ 7

Author(s):

JOHN ERIK FORNÆSS ◽

NESSIM SIBONY

Keyword(s):

Holomorphic Maps ◽

Closing Lemma ◽

Biholomorphic Maps

The closing lemma is proved for various classes of holomorphic self-maps on ${\Bbb C}^k$. These classes include those consisting of biholomorphic maps, endomorphisms and symplectomorphisms.

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