Previous |  Up |  Next


zero-dimensional scheme; cohomology; vector bundle; fat point
Here we give conditions and examples for the surjectivity or injectivity of the restriction map $H^0(X,F)\rightarrow H^0(Z,F\,|\, Z)$, where $X$ is a projective variety, $F$ is a vector bundle on $X$ and $Z$ is a ``general'' $0$-dimensional subscheme of $X$, $Z$ union of general ``fat points''.
[AH] Alexander J., Hirschowitz A.: An asymptotic vanishing theorem for generic unions of multiple points. preprint alg-geom 9703037. MR 1756998 | Zbl 0973.14026
[A] Atiyah M.F.: Vector bundles over an elliptic curve. Proc. London Math. Soc. (3) 7 (1957), 514-452; reprinted in: Michael Atiyah Collected Works, Vol. l, pp.105-143, Oxford Science Publications, Clarendon Press, Oxford, 1988. MR 0131423 | Zbl 0084.17305
[G] Gimigliano A.: Our thin knowledge of fat points. in: Queen's Papers in Pure and Applied Mathematics, vol. 83, The Curves Seminar at Queen's, Vol. VI, 1989. MR 1036032 | Zbl 0743.14005
[HH] Hartshorne R., Hirschowitz A.: Cohomology of a general instanton bundle. Ann. Scient. Ec. Norm. Sup. 15 (1982), 365-362. MR 0683638 | Zbl 0509.14015
[HK] Hein G., Kurke H.: Restricted tangent bundle of space curves. Israel Math. Conf. Proc. 9 (1996), 283-294. MR 1360509
[H1] Hirschowitz A.: Problémes de Brill-Noether en rang supérieur. C.R. Acad. Sci. Paris, Série I, 307 (1988), 153-156. MR 0956606 | Zbl 0654.14017
[H2] Hirschowitz A.: Existence de faisceaux réflexifs de rang deux sur ${\bold P}^3$ à bonne cohomologie. Publ. Math. I.H.E.S. 66 (1988), 105-137. MR 0932136
[H3] Hirschowitz A.: Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles génériques. J. reine angew. Math. 397 (1989), 208-213. MR 0993223
[I1] Iarrobino A.: Inverse systems of a symbolic power III: thin algebras and fat points. preprint, 1994. MR 1473851
[I2] Iarrobino A.: Associated graded algebra of a Gorenstein Artin algebra. Mem. Amer. Math. Soc. 514, 1994. MR 1184062 | Zbl 0793.13010
[N] Neeman A.: Weierstrass points in characteristic $p$. Invent. Math. 75 (1984), 359-376. MR 0732551 | Zbl 0555.14009
[R] Raynaud M.: Sections des fibrés vectoriels sur les courbes. Bull. Soc. Math. France 110 (1982), 103-125. MR 0662131
Partner of
EuDML logo