Affine connections on complex manifolds of algebraic dimension zero
Sorin Dumitrescu (1), Benjamin McKay (2) ((1) Universit\'e C\^ote, d'Azur, Universit\'e de Nice Sophia Antipolis, CNRS, Laboratoire J.A., Dieudonn\'e, Nice, France, (2) University College Cork, Cork, Ireland)
TL;DR
This paper proves that compact complex manifolds with finite fundamental group and algebraic dimension zero cannot have holomorphic affine connections, highlighting a restriction on their geometric structure.
Contribution
It establishes a new non-existence result for holomorphic affine connections on a class of complex manifolds with specific topological and algebraic properties.
Findings
No holomorphic affine connections on such manifolds
Finite fundamental group and algebraic dimension zero imply geometric restrictions
Advances understanding of complex manifold structures
Abstract
We prove that any compact complex manifold with finite fundamental group and algebraic dimension zero admits no holomorphic affine connection.
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