Slicing Correspondences with High Degree Hypersurfaces

2025/06/03 by Banerjee, Ishan
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.02977

Abstract

We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product Y × Y' and intersecting it with X × Y' (for X a sufficiently ample smooth divisor in Y) induces a bijection between two sets of varieties. This may be of independent interest.

Citations

• Error terms for the motives of discriminant complements and a Cayley-Bacharach theorem
• Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors
• Measures of association between algebraic varieties

Related

• Unramified correspondences
• Alignment Correspondences
• Intersections via resolutions
• Low degree subvarieties of universal hypersurfaces
• Simultaneous Uniformization and Algebraic Correspondences