Work

Heights of complete intersections in toric varieties

Year: 2026

Type: article

Abstract: The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their Ronkin functions. Here we extend these results to the 2 -codimensional situation by presenting a limit formula predicting the typical height of the intersection of two hypersurfaces on a toric variety. More precisely, we prove that the height of the intersection cycle of two effective divisors translated by a strict sequence of torsion points converges to an adelic sum of mixed integrals of roof and duals of Ronkin functions. This partially confirms a previous conjecture of the authors about the average height of families of complete intersections in toric varieties.

Source: Revista Matemática Iberoamericana

DOI: 10.4171/rmi/1654

Authors: Roberto Gualdi, Martín Sombra

Institutions: Universitat Politècnica de Catalunya, Institució Catalana de Recerca i Estudis Avançats, Centre de Recerca Matemàtica, Universitat de Barcelona

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond