scholarly journals On the Briançon-Skoda theorem on a singular variety

2010 ◽  
Vol 60 (2) ◽  
pp. 417-432 ◽  
Author(s):  
Mats Andersson ◽  
Håkan Samuelsson ◽  
Jacob Sznajdman
Keyword(s):  
Singular Variety

scholarly journals Reflexive differential forms on singular spaces. Geometry and cohomology

2014 ◽  
Vol 2014 (697) ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Thomas Peternell
Keyword(s):  
Differential Forms ◽  
Extension Theorem ◽  
Singular Variety ◽  
Singular Spaces ◽  
Complex Spaces ◽  
Rationally Connected ◽  
Smooth Locus ◽  
Recent Extension ◽  
Rationally Connected Varieties

AbstractBased 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.

scholarly journals ON A SINGULAR VARIETY ASSOCIATED TO A POLYNOMIAL MAPPING

2013 ◽  
Author(s):  
Thi Bich Thuy Nguyen ◽  
Anna Valette ◽  
Guillaume Valette
Keyword(s):  
Polynomial Mapping ◽  
Singular Variety

scholarly journals Chern Classes of Projective Modules

1963 ◽  
Vol 23 ◽  
pp. 121-152 ◽  
Author(s):  
Hideki Ozeki
Keyword(s):  
Vector Bundle ◽  
Cross Sections ◽  
Chern Class ◽  
Vector Bundles ◽  
Stein Manifold ◽  
Projective Modules ◽  
Singular Variety ◽  
Differentiable Functions ◽  
Holomorphic Vector Bundles ◽  
Differentiable Vector

In topology, one can define in several ways the Chern class of a vector bundle over a certain topological space (Chern [2], Hirzebruch [7], Milnor [9], Steenrod [15]). In algebraic geometry, Grothendieck has defined the Chern class of a vector bundle over a non-singular variety. Furthermore, in the case of differentiable vector bundles, one knows that the set of differentiable cross-sections to a bundle forms a finitely generated projective module over the ring of differentiable functions on the base manifold. This gives a one to one correspondence between the set of vector bundles and the set of f.g.-projective modules (Milnor [10]). Applying Grauert’s theorems (Grauert [5]), one can prove that the same statement holds for holomorphic vector bundles over a Stein manifold.

scholarly journals The Hodge cohomology and cubic equivalences

1984 ◽  
Vol 94 ◽  
pp. 1-41 ◽  
Author(s):  
Hiroshi Saito
Keyword(s):  
Complex Number ◽  
Algebraic Surface ◽  
Projective Variety ◽  
Smooth Projective Variety ◽  
Chow Group ◽  
Geometric Genus ◽  
Singular Variety ◽  
Higher Dimensional ◽  
Hodge Cohomology ◽  
Complex Number Field

In 1969, Mumford [8] proved that, for a complete non-singular algebraic surface F over the complex number field C, the dimension of the Chow group of zero-cycles on F is infinite if the geometric genus of F is positive. To this end, he defined a regular 2-form ηf on a non-singular variety S for a regular 2-form η on F and for a morphism f: S → SnF, where SnF is the 72-th symmetric product of F, and he showed that ηf vanishes if all 0-cycles f(s), s ∈ S, are rationally equivalent. Roitman [9] later generalized this to a higher dimensional smooth projective variety V.

scholarly journals XXI. An account of a remarkable transposition of the viscera. By Matthew Baillie, M. D. In a letter to John Hunter, Esq. F. R. S

1788 ◽  
Vol 78 ◽  
pp. 350-363 ◽  
Keyword(s):  
Human Body ◽  
Royal Society ◽  
Singular Variety ◽  
John Hunter

Dear Sir, A Very singular variety having occurred lately in the structure of the human body, I beg leave to communicate an account of it by your means to the Royal Society, if you should think it worthy of their notice.

scholarly journals Case of a Singular Variety of Hernia,

The Lancet ◽  
1827 ◽  
Vol 8 (203) ◽  
pp. 502-504 ◽  
Author(s):  
B.C. Brodie
Keyword(s):  
Singular Variety
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