On the signed Euler characteristic property for subvarieties of abelian\n varieties

2018/01/10 by Eva Elduque, Elduque, Eva, Christian Geske +3 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1801.03599

Abstract

We give an elementary proof of the fact that a pure-dimensional closed\nsubvariety of a complex abelian variety has a signed intersection homology\nEuler characteristic. We also show that such subvarieties which, moreover, are\nlocal complete intersections, have a signed Euler-Poincare characteristic. Our\narguments rely on the construction of circle-valued Morse functions on such\nspaces, and use in an essential way the stratified Morse theory of\nGoresky-MacPherson. Our approach also applies (with only minor modifications)\nfor proving similar statements in the analytic context, i.e., for subvarieties\nof compact complex tori. Alternative proofs of our results can be given by\nusing the general theory of perverse sheaves.\n

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