Summary
Fix integers k, d, g with g⩾0, d⩾g+3, k>0, 2k<(d−g), d⩾(g(k+1)/k) + k+1. Here we prove that for a general curve X of genus g and a general L ∈ Picd(X), L is normally presented.
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G. Elencwajg -O. Forster,Bounding cohomology groups of vector bundles on P n , Math. Ann.,246 (1980), pp. 251–270.
G. Elencwajg -A. Hirschowitz -M. Schneider,Les fibres uniformes de rang au plus n sur P n (C)sont ceux qu'on croit, in: Vector bundles and differential equations, Proc. Nice (1979), pp. 37–63, Progress in Math., 7, Birkhöuser, Boston (1980).
L. Ein,Stable vector bundles on projective spaces in Char p}>0, Math. Ann.,254 (1980), pp. 53–72.
T.Fujita,Defining equations for certain types of polarised varieties, in: Complex analysis and algebraic geometry, Cambridge University Press (1977), pp. 165–173.
M. L. Green,The canonical ring of a variety of general type, Duke Math. J.,49 (1982), pp. 1087–1113.
M. L. Green,Koszul cohomology and the geometry of projective varieties, J. Differential Geometry,19 (1984), pp. 125–171.
R. Hartshorne,Algebraic geometry, Graduate text in Math., Vol.52, Berlin, Heidelberg, New York, Springer-Verlag (1977).
R. Hartshorne -A. Hirschowitz,Cohomology of general instanton bundle, Ann. Ec. Norm. Sup.,15 (1982), pp. 365–390.
R. Hartshorne -A. Hirschowitz,Smoothing algebraic space curves, in: Algebraic Geometry-Sitgers (1983), Lecture Notes in Math.,1124, Springer-Verlag, Berlin (1985), pp. 98–131.
A.Hirschowitz, Letter to R. Hartshorne of 12th August 1983.
M.Idá, Thesis at Nice University, June 1986.
H. Lange -G. Martens,Normal generation and presentation of line bundles of low degree on curves, J.f.d.r.u.a. Mathematik (Crelle),356 (1985), pp. 1–18.
M. Maruyama,Elementary transformations of algebraic vector bundles, in: Algebraic geometry-Proceedings, La Rabida, pp. 241–266, Lecture Notes in Math.,961, Springer-Verlag, Berlin (1983).
D. Mumford,Lectures on curves on an algebraic surface, Annals of Math. Studies, n. 59, Princeton University Press, N. J. (1966).
D. Mumford,Varieties defined by quadratic equations, Corso C.I.M.E., 1969, in: Question on Algebraic Varieties, ed. Cremonese, Roma (1970), pp. 30–100.
B. St-Donat,Sur les équations definissant une courbe algébrique, C. R. Acad. Sci. Paris, Ser. A,274 (1972), pp. 324–327.
F. O.Schreyer,Syzygies of curves with special pencils, Thesis at Brandeis Univ. (1983).
F. O. Schreyer,Syzygies of canonical curves and special linear series, Math. Ann.,275 (1986), pp. 105–137.
E. Sernesi,On the existence of certain families of curves, Invent. Math.,75 (1984), pp. 25–57.
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Ballico, E. On the homogeneous ideal of projectively normal curves. Annali di Matematica pura ed applicata 154, 83–90 (1989). https://doi.org/10.1007/BF01790343
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DOI: https://doi.org/10.1007/BF01790343