Curves in low dimensional projective spaces with the lowest ranks

Abstract Let X ⊂ ℙr be an integral and non-degenerate curve. For each q ∈ ℙr the X-rank r X (q) of q is the minimal number of points of X spanning q. A general point of ℙr has X-rank ⌈(r + 1)/2⌉. For r = 3 (resp. r = 4) we constr...

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Autor principal:	Ballico,Edoardo
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2020
Materias:	X-rank projective curve space curve curve in projective spaces.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300379
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spelling	oai:scielo:S0719-064620200003003792020-12-30Curves in low dimensional projective spaces with the lowest ranksBallico,Edoardo X-rank projective curve space curve curve in projective spaces. Abstract Let X ⊂ ℙr be an integral and non-degenerate curve. For each q ∈ ℙr the X-rank r X (q) of q is the minimal number of points of X spanning q. A general point of ℙr has X-rank ⌈(r + 1)/2⌉. For r = 3 (resp. r = 4) we construct many smooth curves such that r X (q) ≤ 2 (resp. r X (q) ≤ 3) for all q ∈ ℙr (the best possible upper bound). We also construct nodal curves with the same properties and almost all geometric genera allowed by Castelnuovo’s upper bound for the arithmetic genus.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.22 n.3 20202020-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300379en10.4067/S0719-06462020000300379
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	X-rank projective curve space curve curve in projective spaces.
spellingShingle	X-rank projective curve space curve curve in projective spaces. Ballico,Edoardo Curves in low dimensional projective spaces with the lowest ranks
description	Abstract Let X ⊂ ℙr be an integral and non-degenerate curve. For each q ∈ ℙr the X-rank r X (q) of q is the minimal number of points of X spanning q. A general point of ℙr has X-rank ⌈(r + 1)/2⌉. For r = 3 (resp. r = 4) we construct many smooth curves such that r X (q) ≤ 2 (resp. r X (q) ≤ 3) for all q ∈ ℙr (the best possible upper bound). We also construct nodal curves with the same properties and almost all geometric genera allowed by Castelnuovo’s upper bound for the arithmetic genus.
author	Ballico,Edoardo
author_facet	Ballico,Edoardo
author_sort	Ballico,Edoardo
title	Curves in low dimensional projective spaces with the lowest ranks
title_short	Curves in low dimensional projective spaces with the lowest ranks
title_full	Curves in low dimensional projective spaces with the lowest ranks
title_fullStr	Curves in low dimensional projective spaces with the lowest ranks
title_full_unstemmed	Curves in low dimensional projective spaces with the lowest ranks
title_sort	curves in low dimensional projective spaces with the lowest ranks
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300379
work_keys_str_mv	AT ballicoedoardo curvesinlowdimensionalprojectivespaceswiththelowestranks
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Curves in low dimensional projective spaces with the lowest ranks

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