In this note we introduce the notion of (b, d)-geprofi sets and study their basic properties. These are sets of bd points in P4 whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree b and a surface of degree d. We show that such nontrivial sets exist if and only if b≥4 and d≥2. Somewhat surprisingly, for infinitely many values of b and d there exist such sets in linear general position. The note contains open questions and problems.
Chiantini, L., Farnik, Ł., Favacchio, G., Harbourne, B., Migliore, J., Szemberg, T., et al. (2025). Finite sets of points in P4 with special projection properties. GEOMETRIAE DEDICATA, 219(2) [10.1007/s10711-025-00990-y].
Finite sets of points in P4 with special projection properties
Chiantini, Luca
Membro del Collaboration Group
;
2025-01-01
Abstract
In this note we introduce the notion of (b, d)-geprofi sets and study their basic properties. These are sets of bd points in P4 whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree b and a surface of degree d. We show that such nontrivial sets exist if and only if b≥4 and d≥2. Somewhat surprisingly, for infinitely many values of b and d there exist such sets in linear general position. The note contains open questions and problems.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Geprofi.pdf
non disponiibile
Descrizione: File della pubblicazione
Tipologia:
PDF editoriale
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
514.6 kB
Formato
Adobe PDF
|
514.6 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/1305994