2 results
Polar Homology
-
- Journal:
- Canadian Journal of Mathematics / Volume 55 / Issue 5 / 01 October 2003
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1100-1120
- Print publication:
- 01 October 2003
-
- Article
-
- You have access
- Export citation
-
For 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.
Higher Dimensional Harmonic Volume Can be Computed as an Iterated Integral
-
- Journal:
- Canadian Mathematical Bulletin / Volume 35 / Issue 3 / 01 September 1992
- Published online by Cambridge University Press:
- 20 November 2018, pp. 328-340
- Print publication:
- 01 September 1992
-
- Article
-
- You have access
- Export citation
-
In this paper it is shown that the computation of higher dimensional harmonic volume, defined in [1], can be reduced to Harris' computation in the onedimensional case (See [3]), so that higher dimensional harmonic volume may be computed essentially as an iterated integral. We then use this formula to produce a specific smooth curve
, namely a specific double cover of the Fermat quartic, so that the image 
of the second symmetric product of in its Jacobian via the Abel-Jacobi map is algebraically inequivalent to the image of under the group involution on the Jacobian.
, namely a specific double cover of the Fermat quartic, so that the image 
of the second symmetric product of 