The main result of this paper gives a complete classification of complex smooth projective varieties X⊂Pn which are nondegenerate, linearly normal and of degree d≤n. Nondegenerate means that X is not contained in a hyperplane of Pn, and linearly normal means that the map H0(Pn,OPn(1))→H0(X,OX(1)) is surjective. The adjunction mapping plays a key role in the proof, which also relies on previous results by the author [Math. Ann. 271 (1985), no. 3, 339--348; MR0787185 (86j:14031)]. The classification has some interesting consequences. For example, X as above must be either rational or Fano, and, in particular, it is always simply connected.
On manifolds of small degree
IONESCU, Paltin
2008
Abstract
The main result of this paper gives a complete classification of complex smooth projective varieties X⊂Pn which are nondegenerate, linearly normal and of degree d≤n. Nondegenerate means that X is not contained in a hyperplane of Pn, and linearly normal means that the map H0(Pn,OPn(1))→H0(X,OX(1)) is surjective. The adjunction mapping plays a key role in the proof, which also relies on previous results by the author [Math. Ann. 271 (1985), no. 3, 339--348; MR0787185 (86j:14031)]. The classification has some interesting consequences. For example, X as above must be either rational or Fano, and, in particular, it is always simply connected.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
