Linking numbers for algebraic cycles through isolated singularities
Abstract
I develop here a linking number for divisors in normal complex projective surfaces. This number coincides with Mumford's intersection number (11) for divisors in such a surface. I then use my definition for linking numbers to try to create a higher dimensional analog with algebraic cycles in complex projective varieties having only isolated singularities. My approach succeeds in general for even dimensional spaces (real dimension a multiple of 4) when both cycles have dimension exactly half the total dimension, but requires assumptions about one of the cycles--namely that it must correspond to a torsion element in a particular homology group--otherwise. This assumption is automatically true when the singularity is a quotient singularity. I conclude with the calculation of my linking number for a few examples, then I describe further directions this work could proceed along.
Degree
Ph.D.
Advisors
Arapura, Purdue University.
Subject Area
Mathematics
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