TY - CHAP
T1 - Some intrinsic constructions on compact Riemann surfaces
AU - Gunning, Robert Clifford
PY - 2013/9/2
Y1 - 2013/9/2
N2 - For any prescribed differential principal part on a compact Riemann surface, there are uniquely determined and intrinsically defined meromorphic abelian differentials with these principal parts, defined independently of any choice of a marking of the surface or of a basis for the holomorphic abelian differentials, and they are holomorphic functions of the singularities. They can be constructed explicitly in terms of intrinsically defined cross-ratio functions on the Riemann surfaces, the classical cross-ratio function for the Riemann sphere, and natural generalizations for surfaces of higher genus.
AB - For any prescribed differential principal part on a compact Riemann surface, there are uniquely determined and intrinsically defined meromorphic abelian differentials with these principal parts, defined independently of any choice of a marking of the surface or of a basis for the holomorphic abelian differentials, and they are holomorphic functions of the singularities. They can be constructed explicitly in terms of intrinsically defined cross-ratio functions on the Riemann surfaces, the classical cross-ratio function for the Riemann sphere, and natural generalizations for surfaces of higher genus.
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U2 - 10.1007/978-1-4614-4075-8_13
DO - 10.1007/978-1-4614-4075-8_13
M3 - Chapter
AN - SCOPUS:84883063640
SN - 9781461440741
T3 - Developments in Mathematics
SP - 303
EP - 324
BT - From Fourier Analysis and Number Theory to Radon Transforms and Geometry
A2 - Farkas, Hershel
A2 - Knopp, Marvin
A2 - Gunning, Robert
A2 - Taylor, B.A
ER -