A Weak (k,k)-Lefschetz Theorem for Projective Toric Orbifolds

2023/02/07 by William D. Montoya, Montoya, William D.
Mathematics · #14C30 #14J70 #14M10 #14M25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2302.03803

openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Firstly we show a generalization of the (1,1)-Lefschetz theorem for projective toric orbifolds and secondly we prove that on 2k-dimensional quasi-smooth hypersurfaces coming from quasi-smooth intersection surfaces, under the Cayley trick, every rational (k,k)-cohomology class is algebraic, i.e., the Hodge conjecture holds on them.

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