A set K of type (m,n)2 in the projective space PG(3,q) is a set of points such that every plane contains either m or n points of K. In [22] Vito Napolitano and Domenico Olanda provide a complete classification of sets of type (3,q+3)2 in PG(3,q). In particular, PG(3,3) contains, up to projective equivalence, exactly three, one of size 12 and two of size 15, sets of type (3,6)2, containing no line. It is easy to verify that the 12-set is a vertexless tetraedro, while in [30], Fulvio Zuanni give a nice geometric description of the two 15-sets. In this paper we provide three new different descriptions of one of them, Example 4.2 pag. 401 of [22]
Three different names of a 15-set of type (3,6)2 in PG(3,3)
Daniela Tondini
2018-01-01
Abstract
A set K of type (m,n)2 in the projective space PG(3,q) is a set of points such that every plane contains either m or n points of K. In [22] Vito Napolitano and Domenico Olanda provide a complete classification of sets of type (3,q+3)2 in PG(3,q). In particular, PG(3,3) contains, up to projective equivalence, exactly three, one of size 12 and two of size 15, sets of type (3,6)2, containing no line. It is easy to verify that the 12-set is a vertexless tetraedro, while in [30], Fulvio Zuanni give a nice geometric description of the two 15-sets. In this paper we provide three new different descriptions of one of them, Example 4.2 pag. 401 of [22]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
