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M.S. Narasimhan has been one of the major figures in Mathematics over the last five decades, having made fundamental contributions to diverse areas such as Algebraic Geometry, Differential Geometry, Representation Theory and Analysis. He is one of the principal architects of the School of Mathematics at the Tata Institute of Fundamental Research. He has also played an important role in the progress that India has made in Mathematics in these years.
Even as he approaches the age of 75 next year, Narasimhan continues to be active as a researcher, as an organiser and as a mentor for young researchers. The Tata Institute of Fundamental Research is happy to publish this 2volume book of his collected papers. In addition to its value to the worldwide mathematical community, it is a token expression of our gratitude for all that he has done for the School of mathematics, TIFR.
Contents :
Volume I
Editorial Preface
Curriculum Vitae
A Brief Summary of the Work of M.S. Narasimhan
M.S. Narasimhan and his Work by C.S. Seshadri
Acknowledgements:
1. The problem of limits on a Riemannian manifold, J. Indian Math. Soc. (N.S.) 20 (1956), 291--297.
2. The identity of the weak and strong extensions of a linear elliptic differential operator, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 513--514.
3. The identity of the weak and strong extensions of a linear elliptic differential operator. II, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 620.
4. The type and the Green's kernel of an open Riemann surface, Ann. Inst. Fourier. Grenoble 10 (1960), 285--296.
5. Variations of complex structures on an open Riemann surface, Ann. Inst. Fourier Grenoble 11 (1961), 493--514, XVI--XVII.
6. Existence of universal connections (with S. Ramanan), Amer. J. Math. 83 (1961), 563-572.
7. Existence of universal connections, II (with S. Ramanan), Amer. J. Math. 85 (1963), 223--231.
8. Regularity theorems for fractional powers of a linear elliptic operator (with Takeshi Kotake), Bull. Soc. Math. France 90 (1962), 449--471.
9. Stable bundles and unitary bundles on a compact Riemann surface (with C.S. Seshadri), Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 207--211.
10. Holomorphic vector bundles on a compact Riemann surface (with C.S. Seshadri), Math. Ann. 155 (1964), 69--80.
11. Stable and unitary vector bundles on a compact Riemann surface (with C.S. Seshadri), Ann. of Math. (2) 82 (1965), 540--567.
12. Manifolds with ample canonical class (with R.R. Simha), Invent. Math. 5 (1968), 120--128.
13. Vector bundles on curves (with S. Ramanan), Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) pp. 335--346 Oxford Univ. Press, London, 1968.
14. Moduli of vector bundles on a compact Riemann surface (with S. Ramanan), Ann. of Math. (2) 89 (1969), 14--51.
15. An analogue of the BorelWeilBott theorem for hermitian symmetric pairs of noncompact type (with K. Okamoto), Ann. of Math. (2) 91 (1970), 486--511.
16. Geometry of moduli spaces of vector bundles, Actes du Congres International des Mathematiciens (Nice, 1970), Tome 2, pp. 199-201. GauthierVillars, Paris, 1971.
17. On the cohomology groups of moduli spaces of vector bundles on curves (with G. Harder), Math. Ann. 212 (1975), 215--248.
18. Deformations of the moduli space of vector bundles over an algebraic curve (with S. Ramanan), Ann. of Math. (2) 101 (1975), 391--417.
19. Generalised Prym varieties as fixed points (with S. Ramanan), J. Indian Math. Soc. (N.S.) 39 (1975), 1--19.
20. Geometry of Hecke cycles, I (with S. Ramanan), C.P. Ramanujam---a tribute, pp. 291--345, Tata Inst. Fund. Res. Studies in Math., 8 Springer, BerlinNew York, 1978.
21. Geometry of SU(2) gauge fields (with T.R. Ramadas), Comm. Math. Phys. 67 (1979), no. 2, 121--136.
22. Polarisations on an abelian variety (with M.V. Nori), Proc. Indian Acad. Sci. Math. Sci. 90 (1981), no. 2, 125--128.
23. Fibres de 't Hooft speciaux et applications (with A. Hirschowitz), (French) [Special 't Hooft bundles and applications] Enumerative geometry and classical algebraic geometry (Nice, 1981), pp. 143-164, Progr. Math., 24 Birkhauser, Boston, Mass., 1982.
24. Projective bundles on a complex torus (with G. Elencwajg), J. Reine Angew. Math. 340 (1983), 1--5.
25. Maximal subbundles of rank two vector bundles on curves (with H. Lange), Math. Ann. 266 (1983), no. 1, 55--72
Contents :
Volume II
26. Survey of vector bundles on curves, Singularities, representation of algebras, and vector bundles (Lambrecht, 1985), 1--8, Lecture Notes in Math., 1273 Springer, Berlin, 1987.
27. 2#linear systems on abelian varieties (with S. Ramanan), Vector bundles on algebraic varieties (Bombay, 1984), 415--427, Tata Inst. Fund. Res. Stud. Math., 11 Tata Inst. Fund. Res., Bombay, 1987.
28. Squares of ample line bundles on abelian varieties (with H. Lange), Exposition. Math. 7 (1989), no. 3, 275--287.
29. Spectral curves and the generalised theta divisor (with Arnaud Beauville and S. Ramanan), J. Reine Angew. Math. 398 (1989), 169--179.
30. Groupe de Picard des varieties de modules de fibres semistables sur les courbes algebriques (with J.M. Drezet), (French) [The Picard group of moduli varieties of semistable bundles over algebraic curves] Invent. Math. 97 (1989), no. 1, 53--94.
31. Compactification of MP3 (0, 2) and Poncelet pairs of conics (with G. Trautmann), Pacific J. Math. 145 (1990), no. 2, 255--365.
32. Rank 2 vector bundles on P 4 with c 1 odd and contact curves (with W. Decker and F.O. Schreyer), Math. Z. 205 (1990), no. 1, 123--136.
33. The Picard group of the compactification of MP3 (0, 2) (with G. Trautmann), J. Reine Angew. Math. 422 (1991), 21--44.
34. Factorisation of generalised theta functions, I (with T.R. Ramadas), Invent. Math. 114 (1993), no. 3, 565--623.
35. Vector bundles as direct images of line bundles (with A. Hirschowitz), K. G. Ramanathan memorial issue. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 1, 191--200.
36. Infinite Grassmannians and moduli spaces of Gbundles (with Shrawan Kumar and A. Ramanathan), Math. Ann. 300 (1994), no. 1, 41--75.
37. Picard group of the moduli spaces of Gbundles (with Shrawan Kumar), Math. Ann. 308 (1997), no. 1, 155--173.
38. Hodge classes of moduli spaces of parabolic bundles over the general curve (with Indranil Biswas), J. Algebraic Geom. 6 (1997), no. 4, 697--715.
39. HermitianEinstein metrics on parabolic stable bundles (with Jia Yu Li), Acta Math. Sin. (Engl. Ser.) 15 (1999), no. 1, 93--114.
40. A note on HermitianEinstein metrics on parabolic stable bundles (with Jia Yu Li), Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 1, 77--80.
41. A generalisation of Nagata's theorem on ruled surfaces (with Yogish I. Holla), Compositio Math. 127 (2001), no. 3, 321--332. 824
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