Collected Papers of C.S. Seshadri, 2 Volume Set (Vector Bundles And Invariant Theory)

Over the past fifty years, C.S. Seshadri has been a towering figure in the mathematical horizon, and his contributions have been central to the development of moduli problems and geometric invariant theory as well as representation theory of algebraic groups. The two volumes of the collected papers have been organised in accordance with the subject matter, reflecting faithfully the diversity of his mathematical contributions.

These volumes will achieve the objective of inspiring future generations of mathematicians and provide insights into the unique mathematical personality of C.S. Seshadri.

Table of Contents

Volume 1: Vector Bundles and Invariant Theory

• Preface
• Curriculum Vitae of C S Seshadri
• List of Publications
• Acknowledgements
• 1. V. Balaji and V. Lakshmibai, C.S. Seshadri's work on vector bundles and invariant theory
• 2. David Gieseker and Jun Li, Non-abelian Jacobians and gauge theory
• 3. Generalised multiplicative meromorphic functions on a complex analyticmanifold Jour. Ind. Math. Soc., 21(1957), 149-175.
• 4. Triviality of vector bundles over the affine space K2, Proc. Nat. Aca. Sci., U.S.A. 44 (1958), 456-458.
• 5. L' operation de Cartier: Applications, Seminaire C. Chevalley, 3e annee, 1958-1959.
• 6. Diviseurs en geometrie algebrique, Seminaire C. Chevalley, 3e annee, 1958-1959.
• 7. Diviseurs en geometrie algebrique (Suite), Seminaire C. Chevalley, 3e annee, 1958-1959.
• 8. Algebraic vector bundles over the product of an a ne curve and the afffine line, Proc. Amer. Math. Soc. 10 (1959), 670-673.
• 9. Variete de Picard d'une variete complete, Annali di Mat.Italy IV, Vol. LVII (1962), 117-142.
• 10. On a theorem of Weitzenbock in invariant theory, J. Math, Kyoto Univ. 1, No.3, (1962), 403-409.
• 11. Some results on the quotient space by an algebraic group of automorphisms, Math. Annalen, 149 (1963), 286-301.
• 12. Quotient space by an Abelian variety, Math. Annalen, 152 (1963), 185-194.
• 13. (with M.S. Narasimhan) Holomorphic vector bundles on a compact Riemann surface, Math. Ann., 155 (1964), 69-80.
• 14. (with M.S. Narasimhan) Stable bundles and unitary bundles on a compact Riemann surface, Proc. Nat. Acad. Soc., 52 (1964), 207-211.
• 15. (with M.S. Narasimhan) Stable bundles and unitary vector bundles on a compact Riemann surface, Annals of Math., 82 (1965), 540-567.
• 16. Universal property of the Picard variety of a complete variety, Math. Ann., 156 (1965), 293-296.
• 17. Space of unitary vector bundles on a compact Riemann surface, Annals of Math., 85 (1967), 303-335.
• 18. Mumford's conjecture for GL(2) and applications, Proc. Intern. Colloquium on Algebraic Geometry, Bombay (1968), 347-371.
• 19. Moduli of vector bundles over an algebraic curve, Questions On algebraic Varieties, C.I.M.E, Varenna, (1969), 139-261.
• 20. Quotient spaces modulo reductive algebraic groups, Annals. of Math., 95, No.3 (1972) 511-556.
• 21. Errata to `Quotient spaces modulo reductive algebraic groups', Annals. of Math. Vol.96, (1972), p.599.
• 22. Theory of moduli, Proc. Symp. in Pure Mathematics, Algebraic Geometry, Arcata, 1974, Amer. Math. Soc. (1975), 265-304.
• 23. Geometric reductivity over arbitrary base, Advances in Maths., 26 (1977) 225-274.
• 24. Moduli of vector bundles on curves with parabolic structures, Bulletin of the Amer. Math. Soc., 83 (1977) 124-126.
• 25. Desingularisation of the moduli varieties of vector bundles on curves, Proc. Tokyo Symposium on Algebraic Geometry, (1977), 155-184.
• 26. (with T. Oda), Compactications of the generalized Jacobian variety, Trans. Amer. Math. Soc. Vol.253, (1979), 1-90.
• 27. (with V.B. Mehta), Moduli of vector bundles on curves with parabolic structures, Math. Ann. 228 (1980) 205-239.
• 28. (with V. Balaji), Cohomology of a moduli space of vector bundles, The Grothendieck Festschrift, Volume 1, Birkhauser, 87-120.
• 29. (with V. Balaji) Poincare polynomials of some moduli varieties, Algebraic Geometry and Analytic Geometry, Springer Verlag (1991) 1-25.
• 30. Vector bundles on curves, Contemporary Mathematics, Volume 153 (1993), 163-200.
• 31. (with D.S. Nagaraj) Degenerations of the moduli spaces of vector bundles on curves I, Proc. Indian Acad. Sci. (Math. Sci.) 107 (1997), 101-137.
• 32. (with D.S. Nagaraj), Degenerations of the moduli spaces of vector bundles on curves II, Proc. Indian Acad. Sci. (Math. Sci.) 109, No.2, (1999), 165-201.
• 33. Degenerations of the moduli spaces of vector bundles on curves, ICTP Lecture Notes 1, (2000), 205-265.
• 34. (with V. Balaji), Semistable principal bundles{I, Journal of Algebra, 258, (2002), 321-347.
• 35. Geometric reductivity (Mumford's Conjecture) revisited, Contemporary Mathematics, Volume 390 (2005), 137-145.
• 36. (with P. Sastry) Geometric Reductivity: A quotient space approach, Journal of the Ramanujan Math. Soc., (to appear in 2011).

Volume 2: Schubert Geometry and Representation Theory

• Preface
• Curriculum Vitae of C S Seshadri
• List of Publications
• Acknowledgements
• 1. Standard Monomial Theory: A Historical Account
• 2. (with V. Lakshmibai & C. Musili) Cohomology of line bundles on G=B, Annales Scientifiques de l'E.N.S, 4 Series, (1974), 89-138.
• 3. Correction to `Cohomology of line bundles on G=B', Annales Scientifiques de l'E.N.S, 4 Series, (1974).
• 4. Cohomology of line bundles on SL3=B, (unpublished), Talk given at the Institute for Advanced Study, (1976).
• 5. Geometry of G=P{I (Theory of standard monomials for minuscule representation), C.P. Ramanujam { A Tribute, TIFR Publication, (1978), 207-239.
• 6. (with V. Lakshmibai), Geometry of G=P{II (The work of De Concini and Procesi and the basic conjectures), Proc. Indian Acad. Sci., 87 A, No.2, (1978), 1-54.
• 7. (with V. Lakshmibai & C. Musili), Geometry of G=P{III (Standard Monomial Theory for a quasi-minuscule P), Proc. Indian Acad. Sci. Vol.87 A, (1979), 93-177.
• 8. (with V. Lakshmibai & C. Musili), Geometry of G=P{IV (Standard Monomial Theory for classical types), Proc. Indian Acad. Sci., Vol. 88 A, (1979), 279-362.
• 9. (with V. Lakshmibai & C. Musili), Geometry of G=P, Bulletin of the Amer. Math. Soc. Vol 1, (1979), 432-435.
• 10. (with C. Musili) Standard Monomial Theory, Lecture Notes in Mathematics, Springer Verlag No. 867, 441-476.
• 11. (with C. Musili), Schubert varieties and the variety of complexes, Volume dedicated to Prof. Shafarevich on his 60th birthday, Birkhauser, 329-359.
• 12. (with V. Lakshmibai), Singular Locus of a Schubert Variety, Bulletin of the Amer. Math. Soc., (1984), 363-366.
• 13. Line bundles on Schubert varieties, International Colloquium on `Vector bundles on algebraic varieties', TIFR, (1984).
• 14. (with V. Lakshmibai), Geometry of G=P{V, Journal of Algebra, Vol. 100, (1986), 462-557.
• 15. The work of P. Littelmann and Standard Monomial Theory, Recent Trends in Mathematics and Physics: A Tribute to Harish Chandra, Narosa, (1995), 178-197.
• 16. (with P. Littelmann), A Pieri{Chevalley type formula for K(G=B) and Standard Monomial Theory, Studies in Memory of Issai Schur, Birkhauser, (2003), 155-176.
• 17. Chevalley: Some Reminiscences, Transformation Groups, No.2-3, (1999), 119-125.
• 18. George Kempf (unpublished).
• 19. M.S.Narasimhan, Collected Papers, Hindustan Book Agency, (2009).

Over the past fifty years, C.S. Seshadri has been a towering figure in the mathematical horizon, and his contributions have been central to the development of moduli problems and geometric invariant theory as well as representation theory of algebraic groups. The two volumes of the collected papers have been organised in accordance with the subject matter, reflecting faithfully the diversity of his mathematical contributions.These volumes will achieve the objective of inspiring future generations of mathematicians and provide insights into the unique mathematical personality of C.S. Seshadri.Table of ContentsVolume 1: Vector Bundles and Invariant Theory Preface Curriculum Vitae of C S Seshadri List of Publications Acknowledgements 1. V. Balaji and V. Lakshmibai, C.S. Seshadri's work on vector bundles and invariant theory 2. David Gieseker and Jun Li, Non-abelian Jacobians and gauge theory 3. Generalised multiplicative meromorphic functions on a complex analyticmanifold Jour. Ind. Math. Soc., 21(1957), 149-175. 4. Triviality of vector bundles over the affine space K2, Proc. Nat. Aca. Sci., U.S.A. 44 (1958), 456-458. 5. L' operation de Cartier: Applications, Seminaire C. Chevalley, 3e annee, 1958-1959. 6. Diviseurs en geometrie algebrique, Seminaire C. Chevalley, 3e annee, 1958-1959. 7. Diviseurs en geometrie algebrique (Suite), Seminaire C. Chevalley, 3e annee, 1958-1959. 8. Algebraic vector bundles over the product of an a ne curve and the afffine line, Proc. Amer. Math. Soc. 10 (1959), 670-673. 9. Variete de Picard d'une variete complete, Annali di Mat.Italy IV, Vol. LVII (1962), 117-142. 10. On a theorem of Weitzenbock in invariant theory, J. Math, Kyoto Univ. 1, No.3, (1962), 403-409. 11. Some results on the quotient space by an algebraic group of automorphisms, Math. Annalen, 149 (1963), 286-301. 12. Quotient space by an Abelian variety, Math. Annalen, 152 (1963), 185-194. 13. (with M.S. Narasimhan) Holomorphic vector bundles on a compact Riemann surface, Math. Ann., 155 (1964), 69-80. 14. (with M.S. Narasimhan) Stable bundles and unitary bundles on a compact Riemann surface, Proc. Nat. Acad. Soc., 52 (1964), 207-211. 15. (with M.S. Narasimhan) Stable bundles and unitary vector bundles on a compact Riemann surface, Annals of Math., 82 (1965), 540-567. 16. Universal property of the Picard variety of a complete variety, Math. Ann., 156 (1965), 293-296. 17. Space of unitary vector bundles on a compact Riemann surface, Annals of Math., 85 (1967), 303-335. 18. Mumford's conjecture for GL(2) and applications, Proc. Intern. Colloquium on Algebraic Geometry, Bombay (1968), 347-371. 19. Moduli of vector bundles over an algebraic curve, Questions On algebraic Varieties, C.I.M.E, Varenna, (1969), 139-261. 20. Quotient spaces modulo reductive algebraic groups, Annals. of Math., 95, No.3 (1972) 511-556. 21. Errata to `Quotient spaces modulo reductive algebraic groups', Annals. of Math. Vol.96, (1972), p.599. 22. Theory of moduli, Proc. Symp. in Pure Mathematics, Algebraic Geometry, Arcata, 1974, Amer. Math. Soc. (1975), 265-304. 23. Geometric reductivity over arbitrary base, Advances in Maths., 26 (1977) 225-274. 24. Moduli of vector bundles on curves with parabolic structures, Bulletin of the Amer. Math. Soc., 83 (1977) 124-126. 25. Desingularisation of the moduli varieties of vector bundles on curves, Proc. Tokyo Symposium on Algebraic Geometry, (1977), 155-184. 26. (with T. Oda), Compactications of the generalized Jacobian variety, Trans. Amer. Math. Soc. Vol.253, (1979), 1-90. 27. (with V.B. Mehta), Moduli of vector bundles on curves with parabolic structures, Math. Ann. 228 (1980) 205-239. 28. (with V. Balaji), Cohomology of a moduli space of vector bundles, The Grothendieck Festschrift, Volume 1, Birkhauser, 87-120. 29. (with V. Balaji) Poincare polynomials of some moduli varieties, Algebraic Geometry and Analytic Geometry, Springer Verlag (1991) 1-25. 30. Vector bundles on curves, Contemporary Mathematics, Volume 153 (1993), 163-200. 31. (with D.S. Nagaraj) Degenerations of the moduli spaces of vector bundles on curves I, Proc. Indian Acad. Sci. (Math. Sci.) 107 (1997), 101-137. 32. (with D.S. Nagaraj), Degenerations of the moduli spaces of vector bundles on curves II, Proc. Indian Acad. Sci. (Math. Sci.) 109, No.2, (1999), 165-201. 33. Degenerations of the moduli spaces of vector bundles on curves, ICTP Lecture Notes 1, (2000), 205-265. 34. (with V. Balaji), Semistable principal bundles{I, Journal of Algebra, 258, (2002), 321-347. 35. Geometric reductivity (Mumford's Conjecture) revisited, Contemporary Mathematics, Volume 390 (2005), 137-145. 36. (with P. Sastry) Geometric Reductivity: A quotient space approach, Journal of the Ramanujan Math. Soc., (to appear in 2011). Volume 2: Schubert Geometry and Representation Theory Preface Curriculum Vitae of C S Seshadri List of Publications Acknowledgements 1. Standard Monomial Theory: A Historical Account 2. (with V. Lakshmibai & C. Musili) Cohomology of line bundles on G=B, Annales Scientifiques de l'E.N.S, 4 Series, (1974), 89-138. 3. Correction to `Cohomology of line bundles on G=B', Annales Scientifiques de l'E.N.S, 4 Series, (1974). 4. Cohomology of line bundles on SL3=B, (unpublished), Talk given at the Institute for Advanced Study, (1976). 5. Geometry of G=P{I (Theory of standard monomials for minuscule representation), C.P. Ramanujam { A Tribute, TIFR Publication, (1978), 207-239. 6. (with V. Lakshmibai), Geometry of G=P{II (The work of De Concini and Procesi and the basic conjectures), Proc. Indian Acad. Sci., 87 A, No.2, (1978), 1-54. 7. (with V. Lakshmibai & C. Musili), Geometry of G=P{III (Standard Monomial Theory for a quasi-minuscule P), Proc. Indian Acad. Sci. Vol.87 A, (1979), 93-177. 8. (with V. Lakshmibai & C. Musili), Geometry of G=P{IV (Standard Monomial Theory for classical types), Proc. Indian Acad. Sci., Vol. 88 A, (1979), 279-362. 9. (with V. Lakshmibai & C. Musili), Geometry of G=P, Bulletin of the Amer. Math. Soc. Vol 1, (1979), 432-435. 10. (with C. Musili) Standard Monomial Theory, Lecture Notes in Mathematics, Springer Verlag No. 867, 441-476. 11. (with C. Musili), Schubert varieties and the variety of complexes, Volume dedicated to Prof. Shafarevich on his 60th birthday, Birkhauser, 329-359. 12. (with V. Lakshmibai), Singular Locus of a Schubert Variety, Bulletin of the Amer. Math. Soc., (1984), 363-366. 13. Line bundles on Schubert varieties, International Colloquium on `Vector bundles on algebraic varieties', TIFR, (1984). 14. (with V. Lakshmibai), Geometry of G=P{V, Journal of Algebra, Vol. 100, (1986), 462-557. 15. The work of P. Littelmann and Standard Monomial Theory, Recent Trends in Mathematics and Physics: A Tribute to Harish Chandra, Narosa, (1995), 178-197. 16. (with P. Littelmann), A Pieri{Chevalley type formula for K(G=B) and Standard Monomial Theory, Studies in Memory of Issai Schur, Birkhauser, (2003), 155-176. 17. Chevalley: Some Reminiscences, Transformation Groups, No.2-3, (1999), 119-125. 18. George Kempf (unpublished). 19. M.S.Narasimhan, Collected Papers, Hindustan Book Agency, (2009).