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Topology of subvarieties of complex semi-abelian varieties. (arXiv:1706.07491v1 [math.AT])
来源于:arXiv
We use the non-proper Morse theory of Palais-Smale to investigate the
topology of smooth closed subvarieties of complex semi-abelian varieties, and
that of their infinite cyclic covers. As main applications, we obtain the
finite generation (except in the middle degree) of the corresponding integral
Alexander modules, as well as the signed Euler characteristic property and
generic vanishing for rank-one local systems on such subvarieties. Furthermore,
we give a more conceptual (topological) interpretation of the signed Euler
characteristic property in terms of vanishing of Novikov homology. As a
byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of
very affine manifolds. Our methods also recast Jun Huh's extension of
Varchenko's conjecture to very affine manifolds, and provide a generalization
of this result in the context of smooth closed subvarieties of semi-abelian
varieties. 查看全文>>