FURTHER fOPERTIES OF ABELIAN INTEGRALS A 'TA CHED 1.n TO ALGEBRAIC VARIETIES

Abstract

In note' I made use of the idea of the product of two constructs in i. ,obtain certain properties of Abelian integrals attached to algebra.. iieties. The present note uses the same method to, obtain further pi perties of such integrals. §1. 1. Let A, B be two homeomorphic absolute manifolds of n dimensions, and consider the product A X B. On this there is a cycle r of n dimensions, homeomorphic to A or B, corresponding to the transformation between A and B implied by their homeomorphism. If a4 (i = 1, Rp), where Rp is the pth Betti number of A, is a base for the p-cycles of A, and b1 (i = 1..., Rp) is the corresponding base for the p-cycles of B, then as, X b_-p (i =1...,Rp; i = 1, . .., Rr_p; p = 0, . .. r) form a base for the r-cycles of A X B. We therefore have

Cite this paper

@inproceedings{Hodge2005FURTHERFO, title={FURTHER fOPERTIES OF ABELIAN INTEGRALS A 'TA CHED 1.n TO ALGEBRAIC VARIETIES}, author={V Hodge and W . V . D . Hodge}, year={2005} }