Variational formulae for Fuchsian groups over families of Algebraic curves (Record no. 48757)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02400nam a2200253Ia 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160627s1998||||xx |||||||||||||| ||und|| |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | UNM Th-54 |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Dakshini, Bhattacharyya |
| Relator term | author |
| 245 ## - TITLE STATEMENT | |
| Title | Variational formulae for Fuchsian groups over families of Algebraic curves |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Year of publication | 1998 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | v; 117p. |
| 502 ## - DISSERTATION NOTE | |
| Dissertation note | 1998 |
| 502 ## - DISSERTATION NOTE | |
| Degree Type | Ph.D |
| 502 ## - DISSERTATION NOTE | |
| Name of granting institution | University of Madras |
| 520 3# - SUMMARY, ETC. | |
| Summary, etc | This thesis contributes to the problem of understanding the uniformizing Fuchsian groups for a family of plane algebraic curves by determining explicit first variational formulae for the generators of the Fuchsian groups say Gt, associated to a l-parameter family of compact Riemann surfaces Xt, where Xt are the Riemann surfaces for the complex algebraic curves arising from a l-parameter family of irreducible polynomials. The main idea of this thesis is to utilize explicit quasiconformal mappings between algebraic curves, calculate the Beltrami coefficients, and hence utilize the Ahlfors-Bers variational formulae when applied to quasiconformal conjugates of Fuchsian groups. The direct practical implementation of the variational formulae that is determined in this thesis is quite feasible. It explains how certain classical Poincare theta series with respect to the initial Fuchsian group can be brought to bear on this problem of applying these variational formulae in a computer package. Although the compact Riemann-surfaces are dealt with and the torsion-free parabolic-free Fuchsian uniformizing group, in this, The Theory of Teichmuller spaces work exactly the same for Riemann surfaces of finite conformal type. It could allow distinguished points or punctures on the compact Riemann surfaces and correspondingly allow elliptic or parabolic elements in the Fuchsian groups under scrutiny, and obtains exactly parallel results. One can directly apply the theorems developed in Chapter IV, to the present case in order to obtain the actual generators of the deformed Fuchsian groups that represent the deformations of the Fermat curves. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Algebraic Curves |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Fuchsian Groups |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Variational Formulae |
| 720 1# - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Nag, Subhashish |
| Relator term | Thesis advisor [ths] |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.imsc.res.in/xmlui/handle/123456789/78 |
| 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 | UNM Th-54 | 45369 | http://www.imsc.res.in/xmlui/handle/123456789/78 | THESIS & DISSERTATION | ||||
| IMSc Library | UNM Th-54 | 36819 | http://www.imsc.res.in/xmlui/handle/123456789/78 | THESIS & DISSERTATION |