期刊
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
卷 2017, 期 3, 页码 715-808出版社
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnw055
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资金
- European Research Council under the European Union's Seventh Framework Programme (FP7)/ERC [247029-SDModels]
A Kokotsakis polyhedron with quadrangular base is a neighborhood of a quadrilateral in a quad surface. Generically, a Kokotsakis polyhedron is rigid. In this article we classify flexible Kokotsakis polyhedra with quadrangular bases. The analysis is based on the fact that any pair of adjacent dihedral angles of a Kokotsakis polyhedron is related by a biquadratic equation. This results in a diagram of branched covers of complex projective lines by elliptic curves. A polyhedron is flexible if and only if all repeated fiber products of coverings meet in the same Riemann surface, which is then the configuration space of the polyhedron.
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