Summary: Modular Equations and
Special Function Transformations
Rob Maier
Depts. of Mathematics and Physics
University of Arizona
Geometry, Topology and Physics Seminar
UCSB
8 February, 2008
High-Level Overview
· Picard­Fuchs equations:
­ Let V

X x be a family of n-dimensional algebraic varieties,
with smooth fibres over the complement of a finite set.
­ Choose a holomorphic n-form on a smooth fibre V0 V, and
n-cycles 1, . . . , r that give a basis for its nth homology.
­ Then can be extended to a meromorphic family of n-forms (x),
and the cycles (homology classes) to (multivalued!) functions of x.
­ The periods i(x)
(x) are multivalued too, but satisfy a Fuchsian

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics