The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>

In this paper, we compute asymptotic invariants—specifically, the Waldschmidt constants and the Seshadri constants—of a set of 31 points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvarian...

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Main Authors: Mikołaj Le Van, Tomasz Szemberg
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/24/3945
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author Mikołaj Le Van
Tomasz Szemberg
author_facet Mikołaj Le Van
Tomasz Szemberg
author_sort Mikołaj Le Van
collection DOAJ
description In this paper, we compute asymptotic invariants—specifically, the Waldschmidt constants and the Seshadri constants—of a set of 31 points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn>3</mn></msup></semantics></math></inline-formula>, defined as the intersection points of a Fermat-type arrangement of planes.
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spelling doaj-art-c9d994bcaf654314a74e8f83ac0a29a72025-08-20T02:43:42ZengMDPI AGMathematics2227-73902024-12-011224394510.3390/math12243945The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>Mikołaj Le Van0Tomasz Szemberg1Department of Mathematics, University of the National Education Commission Krakow, Podchora̧żych 2, 30-084 Kraków, PolandDepartment of Mathematics, University of the National Education Commission Krakow, Podchora̧żych 2, 30-084 Kraków, PolandIn this paper, we compute asymptotic invariants—specifically, the Waldschmidt constants and the Seshadri constants—of a set of 31 points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn>3</mn></msup></semantics></math></inline-formula>, defined as the intersection points of a Fermat-type arrangement of planes.https://www.mdpi.com/2227-7390/12/24/3945Chudnovsky Conjecturelocal positivitylocal effectivitySeshadri constantWaldschmidt constant
spellingShingle Mikołaj Le Van
Tomasz Szemberg
The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
Mathematics
Chudnovsky Conjecture
local positivity
local effectivity
Seshadri constant
Waldschmidt constant
title The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
title_full The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
title_fullStr The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
title_full_unstemmed The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
title_short The Assymptotic Invariants of a Fermat-Type Set of Points in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">P</mi><mn mathvariant="bold">3</mn></msup></semantics></math></inline-formula>
title_sort assymptotic invariants of a fermat type set of points in inline formula math display inline semantics msup mi mathvariant double struck p mi mn mathvariant bold 3 mn msup semantics math inline formula
topic Chudnovsky Conjecture
local positivity
local effectivity
Seshadri constant
Waldschmidt constant
url https://www.mdpi.com/2227-7390/12/24/3945
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