Bounds on the Torsion Subgroups of Néron-Severi Groups

2019/02/07 by Kweon, Hyuk Jun · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.02753

Abstract

Let X \hookrightarrow ℙ^r be a smooth projective variety defined by homogeneous polynomials of degree ≤ d. We give explicit upper bounds on the order of the torsion subgroup (NS X)_tor of the Néron-Severi group of X. The bounds are derived from an explicit upper bound on the number of irreducible components of either the Hilbert scheme Hilb_Q X or the scheme CDiv_n X parametrizing the effective Cartier divisors of degree n on X. We also give an upper bound on the number of generators of (NS X)[ℓ^∞] uniform as ℓ ≠ char k varies.

Cited by

• Complexity of counting points on curves and the factor P₁(T) of the zeta function of surfaces
• Bornes de torsion et un théorème effectif du pgcd

Related

• Bounds on the Torsion Subgroups of Néron-Severi Group Schemes
• Some surfaces with maximal Picard number
• Specialization of Néron-Severi groups in characteristic p
• Torsion in Chow groups of zero cycles of homogeneous projective varieties
• On the Neron-Severi groups of fibered varieties