Bulletin of the American Mathematical Society

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Editors: Vikraman Balaji, V. Lakshmibai, M. Pavaman Murthy and Madhav V. Nori
Title: Collected papers of C. S. Seshadri. Volume 1. Vector bundles and invariant theory
Additional book information: edited by Vikraman Balaji, V. Lakshmibai, M. Pavaman Murthy and Madhav V. Nori, Hindustan Book Agency, New Delhi, India, 2012, xxiv+1008 pp., ISBN 978-93-80250-17-5 (2 volume set)

Editors: Vikraman Balaji, V. Lakshmibai, M. Pavaman Murthy and Madhav V. Nori
Title: Collected papers of C. S. Seshadri. Volume 2. Schubert geometry and representation Theory
Additional book information: edited by Vikraman Balaji, V. Lakshmibai, M. Pavaman Murthy and Madhav V. Nori, Hindustan Book Agency, New Delhi, India, 2012, xxvi+633 pp., ISBN 978-93-80250-17-5 (2 volume set)

M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452. MR 131423, DOI 10.1112/plms/s3-7.1.414

Usha Bhosle, Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves, Ark. Mat. 30 (1992), no. 2, 187–215. MR 1289750, DOI 10.1007/BF02384869

Usha N. Bhosle, On the Narasimhan-Seshadri theorem, Connected at infinity, Texts Read. Math., vol. 25, Hindustan Book Agency, New Delhi, 2003, pp. 36–57. MR 2020871

Usha N. Bhosle, Tensor fields and singular principal bundles, Int. Math. Res. Not. 57 (2004), 3057–3077. MR 2098029, DOI 10.1155/S1073792804133114

R. C. Cowsik and M. V. Nori, Affine curves in characteristic $p$ are set theoretic complete intersections, Invent. Math. 45 (1978), no. 2, 111–114. MR 472835, DOI 10.1007/BF01390268

N. Mohan Kumar, On two conjectures about polynomial rings, Invent. Math. 46 (1978), no. 3, 225–236. MR 499785, DOI 10.1007/BF01390276

V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), no. 3, 205–239. MR 575939, DOI 10.1007/BF01420526

David Mumford, Projective invariants of projective structures and applications, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 526–530. MR 0175899

M. Pavaman Murthy and Jacob Towber, Algebraic vector bundles over $A^{3}$ are trivial, Invent. Math. 24 (1974), 173–189. MR 422276, DOI 10.1007/BF01390050

D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. I, Proc. Indian Acad. Sci. Math. Sci. 107 (1997), no. 2, 101–137. MR 1455315, DOI 10.1007/BF02837721

D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. II. Generalized Gieseker moduli spaces, Proc. Indian Acad. Sci. Math. Sci. 109 (1999), no. 2, 165–201. MR 1687729, DOI 10.1007/BF02841533

M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567. MR 184252, DOI 10.2307/1970710

P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 51, Tata Institute of Fundamental Research, Bombay; Narosa Publishing House, New Delhi, 1978. MR 546290

Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 427303, DOI 10.1007/BF01390008

Pramathanath Sastry and C. S. Seshadri, Geometric reductivity—a quotient space approach, J. Ramanujan Math. Soc. 26 (2011), no. 4, 415–477. MR 2895564

Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 68874, DOI 10.2307/1969915

C. S. Seshadri, Triviality of vector bundles over the affine space $K^{2}$, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 456–458. MR 102527, DOI 10.1073/pnas.44.5.456

C. S. Seshadri, Algebraic vector bundles over the product of an affine curve and the affine line, Proc. Amer. Math. Soc. 10 (1959), 670–673. MR 164972, DOI 10.1090/S0002-9939-1959-0164972-1

C. S. Seshadri, Variété de Picard d’une variété complète, Ann. Mat. Pura Appl. (4) 57 (1962), 117–142 (French). MR 138623, DOI 10.1007/BF02417731

C. S. Seshadri, Some results on the quotient space by an algebraic group of automorphisms, Math. Ann. 149 (1962/63), 286–301. MR 148662, DOI 10.1007/BF01471124

C. S. Seshadri, Quotient space by an abelian variety, Math. Ann. 152 (1963), 185–194. MR 164973, DOI 10.1007/BF01470879

C. S. Seshadri, Fibrés vectoriels sur les courbes algébriques, Astérisque, vol. 96, Société Mathématique de France, Paris, 1982 (French). Notes written by J.-M. Drezet from a course at the École Normale Supérieure, June 1980. MR 699278

A. A. Suslin, Projective modules over polynomial rings are free, Dokl. Akad. Nauk SSSR 229 (1976), no. 5, 1063–1066 (Russian). MR 0469905

L. Szpiro, Lectures on equations defining space curves, Tata Institute of Fundamental Research, Bombay; Springer-Verlag, Berlin-New York, 1979. Notes by N. Mohan Kumar. MR 572085

André Weil, Généralisation des fonctions abéliennes, J. Math. Pure et Appl., 17 (1938), 47-87.

• M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452. MR 0131423 (24 \#A1274)
• Usha Bhosle, Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves, Ark. Mat. 30 (1992), no. 2, 187–215. MR 1289750 (95g:14022), DOI 10.1007/BF02384869
• Usha N. Bhosle, On the Narasimhan-Seshadri theorem, Connected at Infinity, Texts Read. Math., vol. 25, Hindustan Book Agency, New Delhi, 2003, pp. 36–57. MR 2020871 (2006a:14053)
• Usha N. Bhosle, Tensor fields and singular principal bundles, Int. Math. Res. Not. 57 (2004), 3057–3077. MR 2098029 (2006f:14048), DOI 10.1155/S1073792804133114
• R. C. Cowsik and M. V. Nori, Affine curves in characteristic $p$ are set theoretic complete intersections, Invent. Math. 45 (1978), no. 2, 111–114. MR 0472835 (57 \#12525)
• N. Mohan Kumar, On two conjectures about polynomial rings, Invent. Math. 46 (1978), no. 3, 225–236. MR 499785 (80c:13010), DOI 10.1007/BF01390276
• V. B. Mehta and C. S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), no. 3, 205–239. MR 575939 (81i:14010), DOI 10.1007/BF01420526
• David Mumford, Projective invariants of projective structures and applications, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 526–530. MR 0175899 (31 \#175)
• M. Pavaman Murthy and Jacob Towber, Algebraic vector bundles over $A^{3}$ are trivial, Invent. Math. 24 (1974), 173–189. MR 0422276 (54 \#10267)
• D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. I, Proc. Indian Acad. Sci. Math. Sci. 107 (1997), no. 2, 101–137. MR 1455315 (98f:14008)
• D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. II. Generalized Gieseker moduli spaces, Proc. Indian Acad. Sci. Math. Sci. 109 (1999), no. 2, 165–201. MR 1687729 (2000c:14046), DOI 10.1007/BF02841533
• M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567. MR 0184252 (32 \#1725)
• P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 51, Tata Institute of Fundamental Research, Bombay, 1978. MR 546290 (81k:14002)
• Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 0427303 (55 \#337)
• Pramathanath Sastry and C. S. Seshadri, Geometric reductivity—a quotient space approach, J. Ramanujan Math. Soc. 26 (2011), no. 4, 415–477. MR 2895564 (2012k:14060)
• Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 0068874 (16,953c)
• C. S. Seshadri, Triviality of vector bundles over the affine space $K^{2}$, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 456–458. MR 0102527 (21 \#1318)
• C. S. Seshadri, Algebraic vector bundles over the product of an affine curve and the affine line, Proc. Amer. Math. Soc. 10 (1959), 670–673. MR 0164972 (29 \#2263)
• C. S. Seshadri, Variété de Picard d’une variété complète, Ann. Mat. Pura Appl. (4) 57 (1962), 117–142 (French). MR 0138623 (25 \#2066)
• C. S. Seshadri, Some results on the quotient space by an algebraic group of automorphisms, Math. Ann. 149 (1962/1963), 286–301. MR 0148662 (26 \#6169)
• C. S. Seshadri, Quotient space by an abelian variety, Math. Ann. 152 (1963), 185–194. MR 0164973 (29 \#2264)
• C. S. Seshadri, Fibrés vectoriels sur les courbes algébriques (Vector bundles over algebraic curves), Astérisque, vol. 96, Société Mathématique de France, Paris, 1982 (French). Notes written by J.-M. Drezet from a course at the École Normale Supérieure, June 1980. MR 699278 (85b:14023)
• A. A. Suslin, Projective modules over polynomial rings are free, Dokl. Akad. Nauk SSSR 229 (1976), no. 5, 1063–1066 (Russian). MR 0469905 (57 \#9685)
• L. Szpiro, Lectures on equations defining space curves, Tata Institute of Fundamental Research, Bombay, 1979. Notes by N. Mohan Kumar. MR 572085 (82d:14017)
• André Weil, Généralisation des fonctions abéliennes, J. Math. Pure et Appl., 17 (1938), 47-87.