Access the full text.
Sign up today, get DeepDyve free for 14 days.
F. Campana, T. Peternell, M. Toma (2004)
GEOMETRIC STABILITY OF THE COTANGENT BUNDLE AND THE UNIVERSAL COVER OF A PROJECTIVE MANIFOLDBulletin de la Société Mathématique de France, 139
B. Totaro (2010)
Algebraic surfaces and hyperbolic geometryarXiv: Algebraic Geometry
Sandor Kovacs, Karl Schwede, Karen Smith (2008)
The canonical sheaf of Du Bois singularitiesAdvances in Mathematics, 224
D. Greb, S. Rollenske (2010)
Torsion and cotorsion in the sheaf of KarXiv: Algebraic Geometry
J. Koll´ar (2008)
Is There a Topological Bogomolov–miyaoka–yau Inequality?
L. Beshaj (2022)
Algebraic GeometryNew Spaces in Mathematics
J. Huizenga (2009)
RATIONALLY CONNECTED VARIETIES
(1995)
Singularities of pairs, Algebraic geometry-Santa Cruz
F. Campana, H. Flenner (2001)
Contact singularitiesmanuscripta mathematica, 108
To appear in the "Handbook of Moduli, in honour of David Mumford
L. Illusie (1977)
Séminaire de Géométrie Algébrique du Bois-Marie 1965–66 SGA 5
Y. Namikawa (2000)
Deformation theory of singular symplectic n-foldsMathematische Annalen, 319
D. Greb, Stefan Kebekus, S'andor Kov'acs (2008)
Extension theorems for differential forms and Bogomolov–Sommese vanishing on log canonical varietiesCompositio Mathematica, 146
A. Grothendieck, J. Dieudonne (1960)
Éléments de géométrie algébriquePublications Mathématiques de l'Institut des Hautes Études Scientifiques, 20
H. Esnault, E. Viehweg (1986)
Logarithmic de Rham complexes and vanishing theoremsInventiones mathematicae, 86
Stefan Kebekus (2011)
Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacksarXiv: Algebraic Geometry
Y. Miyaoka, T. Peternell (2004)
Geometry of Higher Dimensional Algebraic Varieties
A. Grothendieck (1960)
Éléments de géométrie algébrique : I. Le langage des schémasPublications Mathématiques de l'IHÉS, 4
Y. Akizuki, S. Nakano (1954)
Note on Kodaira-Spencer's proof of Lefschetz theorems, 30
A. Meyers (1999)
ReadingOtolaryngology–Head and Neck Surgery, 137
D. Huybrechts, M. Lehn (1997)
The geometry of moduli spaces of sheaves
Christopher Hacon, J. McKernan (2005)
On Shokurov's rational connectedness conjectureDuke Mathematical Journal, 138
T. Murayama (2016)
THE MINIMAL MODEL PROGRAM
D. Gorenstein, M. Rosenlicht, M. Artin (1969)
Algebraic approximation of structures over complete local ringsPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 36
M. Atiyah, I. MacDonald (1969)
Introduction to commutative algebra
Sandor Kovacs (1999)
Rational, Log Canonical, Du Bois Singularities: On the Conjectures of Kollár and SteenbrinkCompositio Mathematica, 118
C. Voisin, Leila Schneps (2002)
Hodge Theory and Complex Algebraic Geometry I: The Hodge Decomposition
A. Grothendieck (1971)
Revetements etales et groupe fondamental
D. Arapura (1988)
Vanishing theorems for $V$-manifolds, 102
C. Okonek, Michael Schneider, H. Spindler (1980)
Vector bundles on complex projective spaces
Shigeetj Iitaka (2010)
Birational Geometry of Algebraic Varieties
M. Artin (2015)
Algebraization of formal moduli: I
D. Greb, Stefan Kebekus, Sandor Kovacs, T. Peternell (2010)
Differential forms on log canonical spacesPublications mathématiques de l'IHÉS, 114
M. Artin (1970)
Algebraization of Formal Moduli: II. Existence of ModificationsAnnals of Mathematics, 91
(1985)
Steenbrink, Vanishing theorems on singular spaces, Astérisque
Y. Kawamata (1988)
Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfacesAnnals of Mathematics, 127
M. Raynaud (1971)
Geometrie Algebrique Et Geometrie Analytique
C. Ramanujam (1974)
Supplement to the Article "Remarks on the Kodaira Vanishing Theorem"Journal of the Indian Mathematical Society, 38
Fouad Elzein, L. Tráng (2013)
Mixed Hodge StructuresTransactions of the American Mathematical Society, 275
P. Wilson (2000)
BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES (Cambridge Tracts in Mathematics 134) By J áNOS K OLLáR and S HIGEFUMI M ORI : 254 pp., £30.00, ISBN 0 521 63277 3 (Cambridge University Press, 1998).Bulletin of The London Mathematical Society, 32
(2002)
Algebraic topology, Cambridge University Press, Cambridge, 2002, available from the author’s home page at http://www.math.cornell.edu/~hatcher
H. Grauert, O. Riemenschneider (1970)
Verschwindungssätze für analytische Kohomologiegruppen auf komplexen RäumenInventiones mathematicae, 11
R. Hartshorne (1968)
Cohomological Dimension of Algebraic VarietiesAnnals of Mathematics, 88
Abstract Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive differentials. First, we generalise the extension theorem to holomorphic forms on locally algebraic complex spaces. We investigate the (non-)existence of reflexive pluri-differentials on singular rationally connected varieties, using a semistability analysis with respect to movable curve classes. The necessary foundational material concerning this stability notion is developed in an appendix to the paper. Moreover, we prove that Kodaira–Akizuki–Nakano vanishing for sheaves of reflexive differentials holds in certain extreme cases, and that it fails in general. Finally, topological and Hodge-theoretic properties of reflexive differentials are explored.
Journal für die reine und angewandte Mathematik – de Gruyter
Published: Dec 1, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.