Polar Homology

2003 ◽  
Vol 55 (5) ◽  
pp. 1100-1120 ◽  
Author(s):  
Boris Khesin ◽  
Alexei Rosly
Keyword(s):  
Boundary Operator ◽  
Homology Groups ◽  
Complex Dimension ◽  
Linking Numbers ◽  
Complex Submanifolds ◽  
Projective Manifolds ◽  
Complex Projective

AbstractFor complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincaré residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions.

scholarly journals Maximal totally complex submanifolds of ℍℙ n : homogeneity and normal holonomy

2009 ◽  
Vol 41 (6) ◽  
pp. 1029-1040 ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori ◽  
Fabio Podestà
Keyword(s):  
Complex Submanifolds
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