Automorphisms of Riemann surfaces of genus g > or = 2 (Record no. 48833)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 01695nam a2200241Ia 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160627s2012||||xx |||||||||||||| ||und|| |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | HBNI MSc 9 |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Arghya Mondal |
| Relator term | author |
| 245 ## - TITLE STATEMENT | |
| Title | Automorphisms of Riemann surfaces of genus g > or = 2 |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Year of publication | 2012 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 45p. |
| 502 ## - DISSERTATION NOTE | |
| Dissertation note | 2012 |
| 502 ## - DISSERTATION NOTE | |
| Degree Type | M.Sc |
| 502 ## - DISSERTATION NOTE | |
| Name of granting institution | HBNI |
| 520 3# - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Automorphisms |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Riemann Surfaces |
| 720 1# - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Nagaraj, D. S. |
| Relator term | Thesis advisor [ths] |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.imsc.res.in/xmlui/handle/123456789/329 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | THESIS & DISSERTATION |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Full call number | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | HBNI MSc 9 | 67565 | http://www.imsc.res.in/xmlui/handle/123456789/329 | THESIS & DISSERTATION |