000			01695nam a2200241Ia 4500
008			160627s2012||||xx |||||||||||||| ||und||
080			_aHBNI MSc 9
100			_aArghya Mondal _eauthor
245			_aAutomorphisms of Riemann surfaces of genus g > or = 2
260			_c2012
300			_a45p.
502			_a2012
502			_bM.Sc
502			_cHBNI
520	3		_aIt 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.
650	1	4	_aMathematics
653	1	0	_aAutomorphisms
653	1	0	_aRiemann Surfaces
720	1		_aNagaraj, D. S. _eThesis advisor [ths]
856			_uhttp://www.imsc.res.in/xmlui/handle/123456789/329
942			_2THESIS128 _cTHESIS _01
999			_c48833 _d48833