Shin-ichi Matsumura (2015)
Complex Manifolds
In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.
Alessandro Silva (1980)
Rendiconti del Seminario Matematico della Università di Padova
W. Barth (1977)
Mathematische Annalen
Paoletti, Roberto (2003)
Advances in Geometry
Michael Schneider (1984)
Mathematische Zeitschrift
R.C. Gunning (1973)
Inventiones mathematicae
Yoshihiro Ohnita, Seiichi Udagawa (1990)
Mathematische Zeitschrift
Xavier Gómez-Mont, George Kempf (1989)
Commentarii mathematici Helvetici
Ruxandra Moraru, Misha Verbitsky (2010)
Open Mathematics
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite...
A. Ramanathan (1975)
Mathematische Annalen
Klaus Hulek (1979)
Mathematische Annalen
Robin Hartshorne (1980)
Mathematische Annalen
Karl Oeljeklaus, Dan Zaffran (2006)
Bulletin de la Société Mathématique de France
Let denote a holomorphic bundle with fiber and with basis . Both and are assumed to be Stein. For a Reinhardt bounded domain of dimension or , we give a necessary and sufficient condition on for the existence of a non-Stein such (Theorem ); for , we give necessary and sufficient criteria for to be Stein (Theorem ). For a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for to be Stein (Theorem ).
Julian Ławrynowicz, Massimo Vaccaro (2011)
Annales UMCS, Mathematica
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...
Paul Gauduchon (1991)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Xiaonan Ma (2000)
Annales de l'institut Fourier
In this paper, we calculate the behaviour of the equivariant Quillen metric by submersions. We thus extend a formula of Berthomieu-Bismut to the equivariant case.
A.T. Huckleberry, J. Winkelmann (1993)
Mathematische Annalen
Vincenzo Ancona (1976)
Rendiconti del Seminario Matematico della Università di Padova
Jean-Michel Bismut (1990)
Inventiones mathematicae
Laurent Manivel (1990)
Bulletin de la Société Mathématique de France