Skip to main content
Log in

Shafarevich maps and plurigenera of algebraic varieties

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

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

Instant access to the full article PDF.

References

  • [A] Atiyah, M.: Vector bundles over an elliptic curve. Proc. Lond. Math. Soc.27, 414–452 (1957)

    Google Scholar 

  • [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact Complex Surfaces. Berlin Heidelberg New York: Springer (1984)

    Google Scholar 

  • [Be] Beauville, A.: Some remarks on Kähler manifolds withc 1=0. In: Ueno, K. (ed.) Classification of algebraic and analytic manifolds, pp. 1–26. Boston Basel Stuttgart: Birkhäuser (1983)

    Google Scholar 

  • [Cam1] Campana, F.: On twistor spaces of the classC. J. Differ. Geom.33, 541–549 (1991)

    Google Scholar 

  • [Cam2] Campana, F.: Connexité rationnelle dés variétés de Fano. Ann. Sci. Éc. Norm. Supér.25, 539–545 (1992)

    Google Scholar 

  • [CatKo] Catanese, F., Kollár, J.: Trento examples 2. In: Classification of Irregular Varieties. (Lect. Notes Math., vol. 1515, pp. 136–139) Berlin Heidelberg New York: Springer 1992

    Google Scholar 

  • [CatTov] Catanese, F., Tovena, F.: Vector bundles with zero discriminant and fundamental groups of algebraic surfaces. In: Complex Algebraic Varieties. (Lect. Notes Math., vol. 1507, pp. 51–70) Berlin Heidelberg New York: Springer 1992

    Google Scholar 

  • [Ch] Chai, C.-L.: Siegel Moduli Schemes and Their Compactification overC. In: Cornell, G., Silverman, J. (eds.) Arithmetic Geometry, pp. 231–251. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  • [D1] Deligne, P.: Théorie de Hodge. Publ. Math., Inst. Hautes Étud. Sci.40, 5–58 (1971)

    Google Scholar 

  • [D2] Deligne, P.: Le groupe fondamental du complément d'une courbe plane n'ayant que des points doubles ordinaires est abélien. Sémmin, Bourbaki # 543, 1979

  • [EV1] Esnault, H., Viehweg, E.: Revêtements cycliques II. In: Aroca, J.-M. et al. (eds.) Géométrie Algèbrique et Applications II, La Rábida, pp. 81–94. Paris: Herman 1987

    Google Scholar 

  • [EV2] Esnault, H., Viehweg, E.: Ample sheaves on moduli schemes. In: Algebraic Geometry and Analytic Geometry, pp. 53–80. Berlin Heidelberg New York: Springer 1991

    Google Scholar 

  • [F] Fletcher, A.: Working with weighted complete intersections. (Preprint, 1989)

  • [GoMacPh] Goresky, M., MacPherson, R.: Stratified Morse Theory. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

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

    Google Scholar 

  • [GriH] Griffiths, P., Harris, J.: Algebraic geometry and local differential geometry. Ann. Sci. Éc. Norm. Supér.12, 355–452 (1979)

    Google Scholar 

  • [Gro] Gromov, M.: Kähler hyperbolicity andL 2-Hodge theory. J. Differ. Geom.33, 263–292 (1991)

    Google Scholar 

  • [Grot] Grothendieck, A.: Fondéments de la Géométrie Algébrique, Sec. Math. Paris, 1962

  • [Gu] Gurjar, R. V.: Coverings of Algebraic Varieties. In: Oda, T. (ed.) Algebraic Geometry, Sendai. (Adv. Stud. Pure Math., vol 10. pp. 179–184) Tokyo Kinokuniya and Amsterdam: North-Holland 1987

    Google Scholar 

  • [I] Iitaka, S.: Genera and classification of algebraic varieties (in Japanese) Sûgaku24, 14–27 (1972)

    Google Scholar 

  • [Ka1] Kawamata, Y.: Characterisation of Abelian varieties. Compos. Math.43, 253–276 (1981)

    Google Scholar 

  • [Ka2] Kawamata, Y.: Minimal models and the Kodaira dimension of algebraic fiber spaces. J. Reine Angew. Math.363, 1–46 (1985)

    Google Scholar 

  • [KaV] Kawamata, Y., Viehweg, E.: On a characterisation of Abelian varieties in the classification theory of algebraic varieties. Compos. Math.41, 355–360 (1980)

    Google Scholar 

  • [KaMM] Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the Minimal Model Problem. In: Oda, T. (ed.) Algebraic Geometry, Sendai. Adv. Stud. Pure Math., vol 10, pp. 283–360) Tokyo: Kinokuniya and Amsterdam: North-Holland 1987

    Google Scholar 

  • [Ko1] Kollár, J.: Higher direct images of dualizing sheaves I.: Ann. Math123, 11–42 (1986); II. Ann. Math124, 171–202 (1986)

    Google Scholar 

  • [Ko2] Kollár, J.: Flips, Flops, Minimal Models, etc. Surv. Differ. Geom.1, 113–199 (1991)

    Google Scholar 

  • [Ko3] Kollár, J.: Effective Base Point Freeness. Math. Ann. (to appear)

  • [Ko et al.] Kollár, J. et. al.: Flips and Abundance for Algebraic Threefolds. (Astérisque, to appear)

  • [KoMiMo] Kollár, J., Miyaoka, Y., Mori, S.: Rationally Connected Varieties. J. Algebraic Geom.1, 429–448 (1992)

    Google Scholar 

  • [L] Laufer, H.: On minimally elliptic singularities. Am. J. Math.99, 1257–1295 (1977)

    Google Scholar 

  • [Mi] Milnor, J.: Singular points of complex hypersurfaces. Princeton University Press 1968

  • [Mo] Mori, S.: Classification of higher-dimensional varieties. In: Bloch, S.J. (ed.) Algebraic Geometry. Bowdoin 1985. (Proc. Symp. Pure Math., vol. 46, pp. 269–332) Providence, RI: Am. Math. Soc. 1987

    Google Scholar 

  • [Mu] Mumford, D.: Abelian Varieties. (Tata Lect. Notes, vol. 5) Oxford: Oxford University Press 1968

    Google Scholar 

  • [N] Nori, M.: Zariski's Conjecture and Related Results. Ann. Sci. Ec. Norm. Supér.16, 305–344 (1983)

    Google Scholar 

  • [Ra] Ran, Z.: Deformations of Calabi-Yau Kleinfolds. In: Essays on Mirror Manifolds, pp. 451–457. New York: International Press 1992

    Google Scholar 

  • [Re1] Reid, M.: Elliptic Gorenstein singularities of surfaces. (University of Warwick Preprint (1976)

  • [Re2] Reid, M.: Canonical Threefolds. In: Beauville, A. (ed.) Géométrie Algébrique Angers, pp. 273–310. Alphen aan den Rijn: Sijthoff & Noordhoff 1980

    Google Scholar 

  • [SGA1] Grothendieck, A.: Revêtements Etales et Groupes Fondamental. (Lect. Notes Math., vol. 224) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  • [Se] Segal, D.: Polycyclic Groups. Cambridge: Cambridge University Press 1983

    Google Scholar 

  • [Sh] Shafarevich, R. I.: Basic Algebraic Geometry (in Russian). Nauka 1972

  • [Si] Siegel, C. L.: Topics in Complex Function Theory, vol. III. New York: Wiley 1973

    Google Scholar 

  • [St] Steenbrink, J. H. M.: Mixed Hodge structures associated with isolated singularities. In: Orlik, P. (ed.) Singularities-Part 2. (Proc. Symp. Pure Math., vol. 40, pp. 513–536) Providence, RI: Am. Math. Soc. 1983

    Google Scholar 

  • [Tol] Toledo, D.: Projective varieties with non-residually finite fundamental group, Publ. Math. Inst. Hautes Étud. Sci. (to appear)

  • [U1] Ueno, K.: Classification Theory of Algebraic Varieties and Compact Complex Spaces. (Lect. Notes Math., vol. 439) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  • [U2] Ueno, K.: Classification of Algebraic II. In: Nagata, M. (ed.) Intl. Symp. Alg. Geom. Kyoto, pp. 693–708. Tokyo: Kinokuniya 1977

    Google Scholar 

  • [V] Viehweg, E.: Weak positivity and the additivity of the Kodaira dimension I. In: Iitaka, S. (ed.), Algebraic varieties and analytic varieties. (Adv. Stud. Pure Math., vol. 1, pp. 329–353) Tokyo: Kinokuniya and Amsterdam: North Holland 1983; II. In: Ueno, K. (ed.) Classification of algebraic and analytic manifolds, pp. 567–590. Boston Basel Stutgart Birkhäuser 1983

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 12-XI-1992 & 10-III-1993

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kollár, J. Shafarevich maps and plurigenera of algebraic varieties. Invent Math 113, 177–215 (1993). https://doi.org/10.1007/BF01244307

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01244307

Keywords

Navigation