Let X be a smooth projective variety and let L be a very ample divisor of X embedding it in ℙN. In this paper we use the Koszul groups of X to get information about the k-normality of X (i.e. the surjectivity of the map H0(ℙN, OℙN(k)) → H0 (X, kL) via an upper bound for the degree of the generators of ⊕t≥0H0(X, tL). The above idea is applied to some scrolls over curves and surfaces and to some other varieties, by using also results due to Green and Butler.
Koszul cohomology and k-normality of a projective variety / A. Alzati, G.M. Besana. - In: BEITRAGE ZUR ALGEBRA UND GEOMETRIE. - ISSN 0138-4821. - 41:1(2000), pp. 279-290.
Koszul cohomology and k-normality of a projective variety
A. AlzatiPrimo
;
2000
Abstract
Let X be a smooth projective variety and let L be a very ample divisor of X embedding it in ℙN. In this paper we use the Koszul groups of X to get information about the k-normality of X (i.e. the surjectivity of the map H0(ℙN, OℙN(k)) → H0 (X, kL) via an upper bound for the degree of the generators of ⊕t≥0H0(X, tL). The above idea is applied to some scrolls over curves and surfaces and to some other varieties, by using also results due to Green and Butler.
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