he speciality theorem of Gruson and Peskine says that if $C \subseteq \bbfP^3$ is a reduced, irreducible curve of degree $d$, not contained in any surface of degree $< t$, and $n$ is an integer such that $H^1 (\bbfP^3, {\cal O}_C (n)) \ne 0$, then $n \le t + (d/t) - 4$, and the equality is attained only if $C$ is a complete intersection (of surfaces of degree $t$ and $d/t)$. In this note, the same theorem is proved with a new, easy proof (based on the use of rank two reflexive sheaves) and which holds also for reducible or not reduced curves.

Some remarks about the speciality theorem of Gruson and Peskine

ROGGERO, Margherita
1985-01-01

Abstract

he speciality theorem of Gruson and Peskine says that if $C \subseteq \bbfP^3$ is a reduced, irreducible curve of degree $d$, not contained in any surface of degree $< t$, and $n$ is an integer such that $H^1 (\bbfP^3, {\cal O}_C (n)) \ne 0$, then $n \le t + (d/t) - 4$, and the equality is attained only if $C$ is a complete intersection (of surfaces of degree $t$ and $d/t)$. In this note, the same theorem is proved with a new, easy proof (based on the use of rank two reflexive sheaves) and which holds also for reducible or not reduced curves.
1985
5-6
253
256
Speciality index; curve; reflexive sheaf
Margherita Roggero
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/2318/103003
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact