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Publications [#287257] of Richard Hain
search www.ams.org.Papers Published
 Hain, RM, The existence of higher logarithms,
Compositio Mathematica, vol. 100 no. 3
(1996),
pp. 247276, ISSN 0010437X [alggeom/9308005]
(last updated on 2018/12/10)
Abstract: In this paper we establish the existence of all higher logarithms as Deligne cohomology classes in a sense slightly weaker than that of [13, Sect. 12], but in a sense that should be strong enough for defining Chem classes on the algebraic Ktheory of complex algebraic varieties. In particular, for each integer p ≥ 1, we construct a multivalued holomorphic function on a Zariski open subset of the self dual grassmannian of pplanes in ℂ2p which satisfies a canonical 2p + 1 term functional equation. The key new technical ingredient is the construction of a topology on the generic part of each Grassmannian which is coarser than the Zariski topology and where each open contains another which is both a K (π, 1) and a rational K (π, 1). © 1996 Kluwer Academic Publishers.


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