TY  - BOOK
AU  - Arghya Mondal
TI  - Automorphisms of Riemann surfaces of genus g > or  = 2
PY  - 2012///
KW  - Mathematics
KW  - Automorphisms
KW  - Riemann Surfaces
N1  - 2012
N2  - It is shown that automorphism group of any Riemann surface X of genus g > or =  2 is finite. Also given a bound to the cardinality of the automorphism group, depending on the genus, speci fically  Aut(X)  < or = 84(g-1). This bound will be obtained by applying Hurwitz formula to the natural holomorphic map from a Riemann surface to it's quotient under action of the  finite group Aut(X). The finiteness  is proved by considering a homomorphism from Aut(X) to the permutation group of a  finite set and showing that the kernel is  finite. The  finite set under consideration is the set of Weierstass points. p is a Weierstass point, if the set of integers n, such that there is no f {element of} M(X) whose only pole is p with order n, is not {1, ... g}. All these are explained in Chapter 4. Riemann-Roch Theorem is heavily  used which is proved in Chapter 3. Proof of Riemann-Roch Theorem requires existence of non-constant meromorphic functions on a Riemann surface, which is proved in Chapter 2. Basics are dealt with in Chapter 1
UR  - http://www.imsc.res.in/xmlui/handle/123456789/329
ER  -