Motives of smooth families and cycles on threefolds

dc.creatorGuletskii, Vladimir
dc.date2005-12-13
dc.date.accessioned2026-07-07T06:55:11Z
dc.date.available2026-07-07T06:55:11Z
dc.descriptionLet X --> S be a smooth projective family of surfaces over a smooth curve S such that the generic fiber is a surface with Weil H^2 spanned by divisors and trivial H^1. We prove that if the relative motive of X/S is finite-dimensional the Chow group CH^2(X) with coefficients in Q is generated by a multisection and vertical cycles, i.e. one-dimensional cycles lying in closed fibers of the map X --> S. If S is the projective line P^1 then CH^2(X) is a direct sum of n+1 copies of Q where n<=b_2 and b_2 is the second Betti number of the generic fiber. Vertical generators in CH^2(X) can be concretely expressed in terms of spreads of algebraic generators of the above H^2. We also show where such families are naturally arising from by spreading out surfaces over C.
dc.identifierhttps://arxiv.org/abs/math/0512292
dc.identifierhttp://arxiv.org/abs/math/0512292
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106201
dc.subjectAlgebraic Geometry
dc.subject14C25
dc.titleMotives of smooth families and cycles on threefolds
dc.typetext

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