Skip to main content
SpringerLink
Log in

Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [Ara] Arakelov, S.J.: Families of algebraic curves with fixed degeneracies. Math. USSR, Izv.5, 1277–1302 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • [At] Atiyah, M.F.: Vector bundles over an elliptic curve. Proc. Lond. Math. Soc., III. Scr.7, 414–452 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  • [Be1] Beauville, A.: Surfaces algébriques complexes. Asterisque54 (1978)

  • [Be2] Beauville, A.: Annullation duH 1 et systemes paracanoniques sur les surfaces. Crelle Jour.388, 149–157 (1988)

    MathSciNet  MATH  Google Scholar 

  • [Be3] Beauville, A.: L'inégalitép g≧2q-4 pour les surfaces de type général. Bull. Soc. Math. Fr.110, 344–346 (1982)

    MathSciNet  Google Scholar 

  • [Bog] Bogomolov, F.: Holomorphic tensors and vector bundles on projective varieties. Math. USSR, Izv.13, 499–555 (1979)

    Article  MATH  Google Scholar 

  • [Bo] Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. I.H.E.S.42, 171–219 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Ergeb. Math. Grenzgeb. 1984

  • [Cas1] Castelnuovo, G.: Sulle superficie aventi il genere aritmetico negativo. Rend. Circ. Math. Palermo20, 55–60 (1905)

    Article  MATH  Google Scholar 

  • [Cas2] Castelnuovo, G.: Sul numero dei moduli di una superficie irregolare. I, II, Rend. Acc. Lincei7, 3–7, 8–11 (1949)

    MathSciNet  MATH  Google Scholar 

  • [Ca1] Catanese, F.: On the moduli spaces of surfaces of general type. J. Differ. Geom.19, 483–515 (1984)

    MathSciNet  MATH  Google Scholar 

  • [Ca2] Catanese, F.: Moduli of surfaces of general type. In: Algebraic Geometry Open Problems. Proceedings Ravello 1982. (Lect. Notes Math., Vol. 997, pp. 90–112) Berlin, Heidelberg, New York: Springer 1983

    Chapter  Google Scholar 

  • [Ca3] Catanese, F.: Moduli of algebraic surfaces, In: Theory of Moduli. Proceedings C.I.M.E. 1985. (Lect. Notes Math., Vol. 1337, pp. 1–83). Berlin, Heidelberg, New York: Springer 1988

    Chapter  Google Scholar 

  • [C-C1] Catanese, F., Ciliberto, C.: Surfaces withp g=q=1. In: “Problems on surfaces and their classification”, Proc. Cortona 1988. Symp. Math.32, INDAM, Academic Press (to appear)

  • [C-C2] Catanese, F., Ciliberto, C.: Symmetric products of elliptic curves and surfaces withp g=q=1. In: Proceedings of the Conf. “Projective Varieties”, Trieste 1989. (Lect. Notes Math.) Berlin, Heidelberg, New York: Springer (to appear)

  • [D-F] De Franchis, M.: Sulle superficie algebriche le quali contengono un fascio irrazionale di curve. Rend. Circ. Mat. Palermo20, 49–54 (1905)

    Article  MATH  Google Scholar 

  • [Des] Deschamps, M.: Reduction semi-stable. In: Seminaire sur les pinceaux de courbes de genre au moins deux. Asterisque86, 1–34 (1981)

    Google Scholar 

  • [Do] Donaldson, S.: La topologie différentièlle des surfaces complexes. C.R. Acad. Sci. Paris301, 317–320 (1985)

    MathSciNet  MATH  Google Scholar 

  • [En] Enriques, F.: Le superficie algebriche. Bologna: Zanichelli 1949

    MATH  Google Scholar 

  • [F1] Flenner, H.: Über Deformationen Holomorpher Abbildungen. Osnabrücker Schriften zur Mathematik I-VII and 1–142 (1979)

  • [Fos] Fossum, R.: Formes differentielles non fermees. In: Seminaire sur les pineaux de courbes de genre au moins deux. Asterisque86, 90–96 (1981)

    Google Scholar 

  • [Fu] Fujita, T.: On Kachler fibre spaces over curves. J. Math. Soc. Japan30, 779–794 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • [Ha] Hartshorne, R.: Algebraic geometry. G.T.M.52. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  • [Ho1] Horikawa, E.: On deformation of holomorphic maps I. J. Math. Soc. Japan25, 372–396 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  • [Ho2] Horikawa, E.: On defermation of holomorphic maps II, J. Math. Soc. Japan26, 647–667 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • [Ho3] Horikawa, E.: On deformation of holomorphic maps III. Math. Ann.222, 275–282 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  • [G-L1] Green, M., Lazarsfeld, R.: Deformation theory, generic vanishing theorems and some conjectures of Enriques, Catanese and Beauville. Invent. Math.90, 389–407 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  • [G-L2] Green, M., Lazarsfeld, R.: Higher obstructions to deforming cohomology groups. Talk at the Trieste Conference “Projective varieties”, June 1989 and paper in preparation

  • [Il1-2] Illusie, L.: Complexe contangent et deformations I, II. (Lect. Notes Math., Vol. 239) 1971, Vol. 283, 1972, Berlin, Heidelberg, New York: Springer

    Book  MATH  Google Scholar 

  • [Il3] Illusie, L.: Complexe de De Rham-Witt et Cohomologie Cristalline. Ann. E.N.S. (4)12, 501–661 (1979)

    MathSciNet  MATH  Google Scholar 

  • [Kaw] Kawamata, Y.: Characterization of Abelian varieties. Comp. Math.43, 253–276 (1981)

    MathSciNet  MATH  Google Scholar 

  • [Ko] Kollar, J.: Higher direct images of dualizing sheaves. Ann. Math., II. Ser.123, 11–42 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • [La] Lang, W.: Quasi-elliptic surfaces in Charasteristic 3. Ann. E.N.S. (4)12, 473–500 (1979)

    Google Scholar 

  • [Me] Menegaux, R.: Un theoreme d'annulation en earacteristique positive. In: Seminaire sur les pinceaux de courbes de genre au moins deux. Asterisque86, 35–43 (1981)

    Google Scholar 

  • [Ny] Nygaard, N.: Closedness of regular 1-forms on algebraic surfaces. Ann. E.N.S. (4)12, 33–45 (1979)

    MathSciNet  MATH  Google Scholar 

  • [Pal] Palamodov, V.P.: Deformations of complex spaces. Usp. Mat. Nauk.31.3, 129–194 (1976)

    MathSciNet  MATH  Google Scholar 

  • [Pet] Peters, C.A.M.: Some remarks about Reider's article ‘On the infinitesimal Torelli theorem for certain irregular surfaces of general type’. Math. Ann.281, 315–324 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • [Ran1] Ran, Z.: On subvarieties of Abelian varieties. Invent. Math.62, 459–479 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • [Ran2] Ran, Z.: Deformations of maps. In: Algebraic Curves and Projective Geometry. Proceedings Trento 1988. (Lect. Notes Math., Vol. 1389, pp. 246–253) Berlin, Heidelberg, New York: Springer 1989

    Chapter  Google Scholar 

  • [Rei] Reider, I.: Bounds for the number of moduli for irregular varieties of general type. Manuscr. Math.60, 221–233 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • [Se] Severi, F.: Geometria dei sistemi algebrici sopra una superficie e sopra una varietá algebrica, Vol. II and III. Roma: Cremonese 1958

    MATH  Google Scholar 

  • [Sh] Shafarevich, I.P.: Algebraic surfaces. Moskva: Steklov Institute Publ. 1965

    MATH  Google Scholar 

  • [Siu] Siu, Y.T.: Strong rigidity for Kaehler manifolds and the construction of bounded holomorphic functions. In: Howe, R. (ed.) Discrete groups and Analysis. Birkhäuser 124–151 (1987)

  • [Sz] Szpiro, L.: Proprietes numeriques du faisceau dualisant relatif. In: Seminaire sur les pinceaux de courbes de genre au moins deux. Asterisque86, 44–78 (1981)

    Google Scholar 

  • [Ueno] Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. (Lect. Notes Math., Vol. 439, Berlin, Heidelberg, New York: Springer 1975

    MATH  Google Scholar 

  • [Y] Yau, S.T.: On the Ricci-curvature of a complex Kaehler manifold and the complex Monge-Ampere equation. Commun. Pure Appl. Math.31, 339–411 (1978)

    Article  MATH  Google Scholar 

References for the Appendix

  • [Be2] Beauville, A.: Annullation deH 1 et systemes paracanoniques sur les surfaces. Crelle Jour.388, 149–157 (1988)

    MathSciNet  MATH  Google Scholar 

  • [Siu] Siu, Y.T.: Strong rigidity for Kaehler manifolds and the construction of bounded holomorphic functions. In: Howe, R. (ed.) Discrete groups and Analysis. Birkhäuser 124–151 (1987)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica della Università di Pisa, via Buonarroti 2, I-56121, Pisa, Italia

    Fabrizio Catanese

Authors
  1. Fabrizio Catanese
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum 18-XII-1989

Rights and permissions

Reprints and permissions

About this article

Cite this article

Catanese, F. Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations. Invent. math. 104, 263–289 (1991). https://doi.org/10.1007/BF01245076

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01245076

Keywords

Search

Navigation