Revista Matemática Iberoamericana· 2026Q1
Heights of complete intersections in toric varieties
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- Q1SCImago
- 2026year
Short summary
A new limit formula predicts the typical height of the intersection of two hypersurfaces in a toric variety, confirming a conjecture about complete intersections.
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Key points
- Height of toric varieties and hypersurfaces expressed via convex-analytic terms.
- Introduced a limit formula for the height of the intersection of two hypersurfaces in a toric variety.
- Height of intersection cycle converges to an adelic sum of mixed integrals of roof and dual Ronkin functions.
- Partially confirms a conjecture on the average height of complete intersections in toric varieties.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Revista Matemática Iberoamericana, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics