论文信息 - Meromorphic Groups

Meromorphic Groups

We introduce the notion of a meromorphic group, weakening somewhat Fujiki’s definition ([4]). We prove that a meromorphic group is meromorphically an extension of a complex torus by a linear algebraic group, generalizing results in [4]. A special case of this result, as well as one of the ingredients in the proof, is that a strongly minimal “modular” meromorphic group is a complex torus, answering a question of Hrushovski. As a consequence, we show that a simple compact complex manifold has algebraic and Kummer dimension zero if and only if its generic type is trivial.

Anand Pillay | Thomas Scanlon

[1] Ehud Hrushovski,et al. Zariski Geometries , 1993 .

[2] R. Moosa. Contributions to the Model Theory of Fields and Compact Complex Spaces , 2001 .

[3] Gerd Fischer,et al. Complex Analytic Geometry , 1976 .

[4] K. Ueno. Classification theory of algebraic varieties and compact complex spaces , 1975 .

[5] S. Bochner,et al. Several complex variables , 1949 .

[6] Oleg V. Belegradek. On groups of finite Morley rank , 1987 .

[7] Wilfrid Hodges,et al. Model Theory: The existential case , 1993 .

[8] Thomas Scanlon,et al. Compact Complex Manifolds with The Dop and Other Properties , 2002, J. Symb. Log..

[9] Akira Fujiki,et al. On automorphism groups of compact Kähler manifolds , 1978 .

[10] Elisabeth Bouscaren,et al. Model Theory and Algebraic Geometry , 1998 .

[11] Chen C. Chang,et al. Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[12] S. Łojasiewicz. Introduction to Complex Analytic Geometry , 1991 .

[13] Ehud Hrushovski,et al. The Mordell-Lang conjecture for function fields , 1996 .

[14] R. Remmert,et al. Several Complex Variables VII , 1994 .

[15] Boris Zilber,et al. Model theory and algebraic geometry , 1993 .

[16] Anand Pillay,et al. Some model theory of compact complex spaces , 2000 .

[17] A. Pillay. Geometric Stability Theory , 1996 .