We study the reciprocal position of nine points in the plane, accordingto their collinearities. In particular, we consider the case in which thenine points are contained in an irreducible cubic curve and we give theirclassification. If we call two configurations different when the associatedincidence structures are not isomorphic, we see that there are 131 config-urations that can be realized inP2Q, and there are two more inP2K, whereK=Q[√−3] (one of the two is the Hesse configuration given by thenine inflection points of a cubic curve). Finally, we compute the possibleHilbert functions of the ideals of the nine points.

On the configurations of nine pointson a cubic curve

Alessandro Logar
;
2021-01-01

Abstract

We study the reciprocal position of nine points in the plane, accordingto their collinearities. In particular, we consider the case in which thenine points are contained in an irreducible cubic curve and we give theirclassification. If we call two configurations different when the associatedincidence structures are not isomorphic, we see that there are 131 config-urations that can be realized inP2Q, and there are two more inP2K, whereK=Q[√−3] (one of the two is the Hesse configuration given by thenine inflection points of a cubic curve). Finally, we compute the possibleHilbert functions of the ideals of the nine points.
2021
Pubblicato
File in questo prodotto:
File Dimensione Formato  
ajc_v79_p087.pdf

accesso aperto

Descrizione: articolo
Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 263.87 kB
Formato Adobe PDF
263.87 kB Adobe PDF Visualizza/Apri
1912.08115.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Digital Rights Management non definito
Dimensione 315.95 kB
Formato Adobe PDF
315.95 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2980384
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact