Tohoku Mathematical Journal
2005
September
SECOND SERIES VOL. 57, NO. 3

Tohoku Math. J.
57 (2005), 395-426

Title COMPACT COMPLEX SURFACES ADMITTING NON-TRIVIAL SURJECTIVE ENDOMORPHISMS

Author Yoshio Fujimoto and Noboru Nakayama

(Received October 22, 2003, revised August 27, 2004)
Abstract. Smooth compact complex surfaces admitting non-trivial surjective endomorphisms are classified up to isomorphism. The algebraic case was dealt with earlier by the authors. The following surfaces are listed in the non-algebraic case: a complex torus, a Kodaira surface, a Hopf surface with at least two curves, a successive blowups of an Inoue surface with curves whose centers are nodes of curves, and an Inoue surface without curves satisfying a rationality condition.

2000 Mathematics Subject Classification. Primary 32J15; Secondary 14J25, 14J27.
Key words and phrases. Endomorphism, elliptic surface, non-algebraic surface, $VII_0$ surface, Kodaira surface, Inoue surface.

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