Report
Heights of complete intersections in toric varieties
| Title: | Heights of complete intersections in toric varieties |
|---|---|
| Authors: | Gualdi, Roberto, Sombra, Martín |
| Source: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Publisher Information: | 2024. |
| Publication Year: | 2024 |
| Subject Terms: | Geometria algèbrica--Aritmètica, Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry, Aritmètica, Arithmetical algebraic geometry, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, Diophantine geometry |
| Description: | 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. ArXiv preprint |
| Document Type: | Report |
| File Description: | application/pdf |
| Language: | English |
| Access URL: | https://hdl.handle.net/2117/427693 https://arxiv.org/abs/2412.16308 https://hdl.handle.net/2117/427693 |
| Accession Number: | edsair.dedup.wf.002..9cfc8cff8ab533889a30edafe261c7dc |
| Database: | OpenAIRE |
| Description not available. |