Subcanonical curves and complete intersections in projective 3-space

Abstract

Un classico teorema di G. Gherardelli afferma che una curvaC P 3 è intersezionè completa se e soltanto se è proiettivamente normale e sottocanonica. Qui si prova che, seC e a- sottocanonica ed inoltre le superficie di grado 1 + (a/2) (a pari) ovvero (a + l)/2 o (a + 3)/2 o (a + 5)/2 (a dispari) tagliano suC serie complete, alloraC è intersezione completa. Si determina inoltre un bound d funzione di a tale che, seC è a-sottocanonica e di grado dles d, alloraC è intersezione completa se e soltanto se le superficie di grado a tagliano suC una serie completa. Si discutono poi numerosi esempi di curve sottocanoniche non intersezioni complete

A Splitting Criterion for Rank 2 Bundles on a General Sextic Threefold

“…Also we would know the geometry of the variety of sextics which have some indecomposable ACM bundles with given Chern classes (somehow an analogue of Noether-Lefschetz loci for surfaces in P 3 ). We finally observe that several numerical refinements of the main result, in the spirit of [8], are immediate using our main theorem and theorem 3.8 of [19]. For instance one gets: …”

Chern classes and cohomology for rank 2 reflexive sheaves on P3

“…First of all put: c = c 2 . By [CV1], Th. 1.6 see n.l, 6), the three nonvanishing groups must correspond to n = -1, 0, 1 therefore a -2 > -2 and a > 0 (see n.l, 6).…”

“…Proof. By [CV1], Prop. 15 (see n.l, 6), the cohomology is not 0 at n = -1 and at n = 0 (to avoid a nullcorrelation bundle, with only one non vanishing group).…”

“…In this case either the 1-cohomology vanishes at 2 values of n or it is a nullcorrelation bundle (see [CV1], Prop. 4).…”

Low Rank Vector Bundles on the Grassmannian G(1,4)

“…However on G(1, 2) and G (1,3) there are notions of regularity (which implies the G-regularity) with finite conditions: the Castelnuovo-Mumford regularity on G(1, 2) ∼ = P 2 and the Qregularity on G(1, 3) ∼ = Q 4 (see [3]). In this paper we consider G (1,4) and we give a notion of regularity with only a finite number of vanishing conditions. Next we show that the L-regularity implies the G-regularity and we prove the analogs of the classical properties on P n+1 .…”