$L^ 2\text {–}\overline \partial$-cohomology of complex projective varieties
HTML articles powered by AMS MathViewer
- by William L. Pardon and Mark A. Stern
- J. Amer. Math. Soc. 4 (1991), 603-621
- DOI: https://doi.org/10.1090/S0894-0347-1991-1102582-6
- PDF | Request permission
References
- Jochen Brüning, Norbert Peyerimhoff, and Herbert Schröder, The $\overline \partial$-operator on algebraic curves, Comm. Math. Phys. 129 (1990), no. 3, 525–534. MR 1051503, DOI 10.1007/BF02097104
- Jeff Cheeger, On the Hodge theory of Riemannian pseudomanifolds, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 91–146. MR 573430
- Jeff Cheeger, Mark Goresky, and Robert MacPherson, $L^{2}$-cohomology and intersection homology of singular algebraic varieties, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 303–340. MR 645745
- Jean-Pierre Demailly, Estimations $L^{2}$ pour l’opérateur $\bar \partial$ d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 3, 457–511 (French). MR 690650, DOI 10.24033/asens.1434
- Harold Donnelly and Charles Fefferman, $L^{2}$-cohomology and index theorem for the Bergman metric, Ann. of Math. (2) 118 (1983), no. 3, 593–618. MR 727705, DOI 10.2307/2006983
- Gerald B. Folland, Introduction to partial differential equations, 2nd ed., Princeton University Press, Princeton, NJ, 1995. MR 1357411
- G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588 G. Gonzales-Springberg, Une formule pour les singularités isoleés de surface, C. R. Acad. Sci. Paris 290 (1980), 475-478.
- Hans Grauert and Reinhold Remmert, Coherent analytic sheaves, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 265, Springer-Verlag, Berlin, 1984. MR 755331, DOI 10.1007/978-3-642-69582-7
- Hans Grauert and Oswald Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math. 11 (1970), 263–292 (German). MR 302938, DOI 10.1007/BF01403182
- Peter Haskell, $L^2$-Dolbeault complexes on singular curves and surfaces, Proc. Amer. Math. Soc. 107 (1989), no. 2, 517–526. MR 975647, DOI 10.1090/S0002-9939-1989-0975647-X
- W. C. Hsiang and V. Pati, $L^2$-cohomology of normal algebraic surfaces. I, Invent. Math. 81 (1985), no. 3, 395–412. MR 807064, DOI 10.1007/BF01388578
- Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775 —, Complex analysis in several variables, Van Nostrand, Princeton, NJ, 1966.
- Masaki Kashiwara and Takahiro Kawai, The Poincaré lemma for variations of polarized Hodge structure, Publ. Res. Inst. Math. Sci. 23 (1987), no. 2, 345–407. MR 890924, DOI 10.2977/prims/1195176545
- Robert MacPherson, Global questions in the topology of singular spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 213–235. MR 804683
- Takeo Ohsawa, Hodge spectral sequence on compact Kähler spaces, Publ. Res. Inst. Math. Sci. 23 (1987), no. 2, 265–274. MR 890919, DOI 10.2977/prims/1195176540
- Takeo Ohsawa, Hodge spectral sequence and symmetry on compact Kähler spaces, Publ. Res. Inst. Math. Sci. 23 (1987), no. 4, 613–625. MR 918517, DOI 10.2977/prims/1195176250
- William L. Pardon, The $L_2$-$\overline \partial$-cohomology of an algebraic surface, Topology 28 (1989), no. 2, 171–195. MR 1003581, DOI 10.1016/0040-9383(89)90019-0
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
- Georges de Rham, Differentiable manifolds, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 266, Springer-Verlag, Berlin, 1984. Forms, currents, harmonic forms; Translated from the French by F. R. Smith; With an introduction by S. S. Chern. MR 760450, DOI 10.1007/978-3-642-61752-2 L. Saper, ${L^2}$-cohomology of Kähler varieties with isolated singularities, preprint. R. O. Wells, Differential analysis on compact manifolds, 2nd ed., Springer-Verlag, Berlin, 1980.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: J. Amer. Math. Soc. 4 (1991), 603-621
- MSC: Primary 32J25; Secondary 14C30, 32S60
- DOI: https://doi.org/10.1090/S0894-0347-1991-1102582-6
- MathSciNet review: 1102582