Abstract
We prove a version of “factorisation”, relating the space of sections of theta bundles on the moduli spaces of (parabolic, rank 2) vector bundles on curves of genusg andg−1.
Similar content being viewed by others
References
Artin, M.: On the solutions of analytic equations. Invent. Math.5, 277–291 (1968)
Atiyah, M.F., Macdonald, I.G.: Introduction to commutative algebra. Reading: Addison-Wesley 1969
Bourbaki, N.: Commutative algebra. Paris: Hermann 1972
Boutot, J.F.: Singularités rationnelles et quotients par les groupes réductifs, Invent. Math.88, 65–68 (1987)
Bhosle, U.: Parabolic vector bundles on curves, Arkiv för matematik27, 15–22 (1989)
Bhosle, U.: Generalised parabolic bundles and applications to torsion-free sheaves on nodal curves. TIFR preprint 1990, to appear in Arkiv för matematik
Donaldson, S.K.: Polynomial invariants for smooth four-manifolds. Topology29, 257–315 (1990)
Drezet, J.M., Narasimhan, M.S.: Groupe de Picard des variétés de fibrés semistables sur les courbes algébriques. Invent. Math.97, 53–94 (1989)
Grauert, H., Riemenschneider, O.: Verschwindungssätze fur analytische Kohomologiegruppen auf komplexen Räumen. Invent. Math.11, 263–292 (1970)
Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométric algébrique IV: les schemas de Hilbert., Exposé 221, Vol. 1960–61, Séminaire Bourbaki
Grothendieck, A.: Cohomologie locale des faisceaux cohérents et théorèmes de lefschetz locaux et globaux (SGA-II). Amsterdam: North-Holland 1968
Grothendieck, A.: Revêtements Étales et Groupe Fondamental (SGA-I). Springer Lecture Notes 224. Berlin-Heidelberg-New York: Springer 1971
Grothendieck, A., Dieudonné, J.: Étude locale des schémas et des morphismes de schémas (iii), Publ. Math. IHES28 (1966)
Grothendieck, A., Dieudonné, J.: Éléments de Géométrie Algébrique I. (new edn.) Grundlehren 166. Berlin-Heidelberg-New York: Springer 1971
Harder, G., Narasimhan, M.S.: On the cohomology groups of the moduli space of vector bundles of on curves. Math. Ann.212, 215–248 (1975)
Hartshorne, R.: Algebraic geometry. Berlin-Heidelberg-New York: Springer 1977
Kempf, G.: Cohomology and covexity, in Kempf G et al. (eds.). Toroidal Imbeddings, Springer Lecture Notes, Vol. 339, Berlin-Heidelberg-New York. Springer, 1973
Knop, F.: Der kanonische Moduleines Invariantenrings. J. Algebra127, 40–54 (1989)
Knudsen, F., Mumford, D.: The projectivity of the moduli space of stable curves I: Preliminaries on “det” and “Div”. Math. Scand.39, 19–55 (1976)
Kraft, H., Procesi, C.: On the geometry of conjugacy classes in classical groups. Comment. Math. Helv.57, 536–602 (1982)
Lang S., Introduction to Arakelov theory. Berlin-Heidelberg-New York: Springer, 1988
Lange, H.: universal families of extensions. J. Algebra83, 101–112 (1983)
Luna, D.: Adehérences d'orbit et invariants. Invent. Math.29, 231–238 (1975)
Matsumura, H.: Commutative ring theory. Cambridge University Press, Cambridge: Cambridge University Press, 1986
Mehta, V.B., Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann.248, 205–239 (1980)
Mumfor, D.: Picard groups of moduli problems. in: Schilling, O.F.G. (ed.) Arithmetical algebraic geometry. New York: Harper and Row
Mumford, D., Fogarty, J.: Geometric invariant theory. 2nd edn. Berlin-Heidelberg-New York.: Springer, 1982
Narasimhan, M.S., Trautmann, G.: Compactification ofM p3 (0, 2) and Poncelet pairs of conics. pacific J. Math.145, 255–365 (1990)
Newstead, P.E.: Introduction to moduli problems and orbit spaces. TIFR lecture notes. New Delhi: Narosa 1978
Ramanan, S.: The moduli spaces of vector bundles over an algebraic curve. Math. Ann.200, 69–84 (1973)
Schiffman, B., Sommense, A.J.: Vanishing theorems on complex manifolds. Boston-Basel-Stuttgart: Birkhaüser 1985.
Serre, J.P.: Géométrie algébrique et géométrie analytique. Ann. Inst., Fourier6, 1–42 (1956)
Seshadri, C.S.: Quotient spaces modulo reductive algebraic groups. Ann. Math.95, 511–556 (1972)
Seshadri, C.S.: Fibrés vectoriels sur les courbes algébriques (Lectures at the E.N.S., notes by J.M. Drezet) Astérisque96 (1982)
Simpson, C.: Moduli of representations of the fundamental group of a smooth projective variety. Princeton University. Preprint 1990
Swan, R.G.: On seminormality. J. Algebra67, 210–229 (1980)
Traverso, C.: Seminormality and Picard group. Ann. Scuola Norm. Sup. Pisa24, 585–595 (1970)
Tsuchiya, A., Ueno, K., Yamada, Y.: Conformal field theory on universal family of stable curves with gauge symmetries. Adv. Studies Pure Math.19, 459–566 (1989)
Zariski, O.: Sur la normalité analytique des variétés normales. Ann. Inst. Fourier (Grenoble)2, 161–164 (1950)
Zariski, O., Samuel, P.: Commutative algebra. II. Princeton: Van Nostrand 1960
Author information
Authors and Affiliations
Additional information
Oblatum 23-I-1992 & 21-VI-1993
Rights and permissions
About this article
Cite this article
Narasimhan, M.S., Ramadas, T.R. Factorisation of generalised theta functions. I. Invent Math 114, 565–623 (1993). https://doi.org/10.1007/BF01232680
Issue Date:
DOI: https://doi.org/10.1007/BF01232680