On the Lefschetz Standard Conjecture

2007/03/01 by Ramón-Marí, José J.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703005

Abstract

The subject of the present paper is Grothendieck's Lefschetz standard conjecture B(X). Our main result is that, if X is a projective smooth variety of dimension n and the conjecture B(\cal Y) holds for the generic fibre \cal Y (of dimension n-1 over the field k(t)) of a suitable Lefschetz fibration of X, then the operator Λ_X-pⁿ⁺¹_X is algebraic. If in addition pⁿ⁺¹_X is algebraic, then B(X) is settled. Along the way we establish the algebraicity of the K" unneth projectors πⁱ_X for i≠ n-1, n, n+1 under the above hypotheses.

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