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Stable vector bundles of rank 2 onP 3

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References

  1. Atiyah, M. F., Rees, E.: Vector bundles on projective 3-space. Invent. math.35, 131–153 (1976)

    Google Scholar 

  2. Atiyah, M.F., Ward, R.S.: Instantons and algebraic geometry. Comm. math. Phys.55, 117–124 (1977)

    Google Scholar 

  3. Atiyah, M.F., Hitchin, N.J., Drinfeld, V.G., Manin, Ju.I.: Construction of instantons. Phys. Lett.65A, 185–187 (1978)

    Google Scholar 

  4. Barth, W., Van de Ven, A.: A decomposability criterion for algebraic 2-bundles on projective spaces. Invent. math.25, 91–106 (1974)

    Google Scholar 

  5. Barth, W., Van de Ven, A.: On the geometry in codimension 2 of Grassmann manifolds. In: Classification of algebraic varieties and compact complex manifolds. Lecture Notes in Mathematics412, pp. 1–35. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  6. Barth, W.: Some properties of stable rank-2 vector bundles on IP n . Math. Ann.226, 125–150 (1977)

    Article  Google Scholar 

  7. Barth, W.: Moduli of vector bundles on the projective plane. Invent. math.42, 63–91 (1977)

    Google Scholar 

  8. Barth, W., Hulek, K.: Monads and moduli of vector bundles (preprint)

  9. Ferrand, D.: Courbes gauches et fibrés de rang 2, C.R. Acad. Sci. (Paris)281, A345–347 (1975)

    Google Scholar 

  10. Ferrand, D.: Construction de fibrés de rang deux. Séminaire E.N.S, (1977–78) exposé 5 (preprint)

  11. Gieseker, D.: On the moduli of vector bundles on an algebraic surface. Ann. Math.106, 45–60 (1977)

    Google Scholar 

  12. Grauert, H., Mülich, G.: Vektorbündel vom Rang 2 über demn-dimensionalen komplex-projektiven Raum. Manusc. math.16, 75–100 (1975)

    Google Scholar 

  13. Grauert, H., Schneider, M.: Komplexe Unterräume und holomorphe Vektorraumbündel vom Rang zwei. Math. Ann.230, 75–90 (1977)

    Google Scholar 

  14. Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométrie algébrique IV: Les schémas de Hilbert. Séminaire Bourbaki221 (1960/61)

  15. Gruson, L., Peskine, C.: Genre des courbes de l'espace projectif (preprint)

  16. Harris, J.: Untitled preprint (Nov. 1976)

  17. Hartshorne, R.: A property of A-sequences. Bull. Soc. Math. France94, 61–66 (1966)

    Google Scholar 

  18. Hartshorne, R.: Varieties of small codimension in projective space. Bull. AMS80, 1017–1032 (1974)

    Google Scholar 

  19. Hartshorne, R.: The classification of curves in IP3 and related topics (lecture notes in Japanese), Ishida, M., Sato, E., eds. Math. Res. Lec. Notes2, Kyoto Univ. 74pp. (1977)

  20. Hartshorne, R.: Algebraic Geometry. Graduate Texts in Math.52, 496pp. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  21. Hartshorne, R.: Stable vector bundles and instantons. Comm. Math. Phys.59, 1–15 (1978)

    Google Scholar 

  22. Hirzebruch, F.: Topological methods in Algebraic Geometry, 3rd ed., Grundlehren der math. Wiss.131, 232 pp. Berlin, Heidelberg, New York: Springer 1966

    Google Scholar 

  23. Horrocks, G.: Vector bundles on the punctured spectrum of a local ring. Proc. Lond. Math. Soc. (3),14, 689–713 (1964)

    Google Scholar 

  24. Horrocks, G.: A construction for locally free sheaves. Topology7, 117–120 (1968)

    Google Scholar 

  25. Horrocks, G., Mumford, D.: A rank 2 vector bundles on IP4 with 15,000 symmetries. Topology12, 63–81 (1973)

    Google Scholar 

  26. Horrocks, G.: Examples of rank three vector bundles on five dimensional projective space (preprint)

  27. Kleiman, S.L.: Geometry on Grassmannians and applications to splitting bundles and smoothing cycles. Publ. Math. IHES36, 281–298 (1969)

    Google Scholar 

  28. Maruyama, M.: On a family of algebraic vector bundles (in) Number Theory, Algebraic Geometry, and Commutative Algebra, in honor of Y. Akizuki. Kinokuniya, Tokyo 95–146 (1965)

  29. Maruyama, M.: Stable vector bundles on an algebraic surface. Nagoya Math. J.58, 25–68 (1975)

    Google Scholar 

  30. Maruyama, M.: Openness of a family of torsion free sheaves. J. Math. Kyoto Univ.16, 627–637 (1976)

    Google Scholar 

  31. Maruyama, M.: Moduli of stable sheaves, I, J. Math., Kyoto Univ.17, 91–126 (1977)

    Google Scholar 

  32. Maruyama, M.: Moduli of stable sheaves, II (preprint)

  33. Mumford, D.: Lectures on curves on an algebraic surface. Annals of Math. Studies59, Princeton Univ. Press, Princeton (1966) 200 pp.

    Google Scholar 

  34. Mumford, D.: Varieties defined by quadratic equations (with an Appendix by G. Kempf) in Questions on Algebraic Varieties. C.I.M.E. ed. Cremonese, Rome (1970), 29–100

    Google Scholar 

  35. Mumford, D.: Theta Characteristics of an algebraic curve. Ann. Sc. ENS4, 181–192 (1971)

    Google Scholar 

  36. Narasimhan, M.S., Seshadri, C.S.: Stable and unitary vector bundles on a compact Riemann Surface. Ann. Math.82, 540–567 (1965)

    Google Scholar 

  37. Peskine, C., Szpiro, L.: Liaison des variétés algébriques (I). Invent. math.26, 271–302 (1974)

    Google Scholar 

  38. Rao, A.P.: Liaison among curves in IP3 (preprint)

  39. Saint-Donat, B.: On Petri's analysis of the linear system of quadrics through a canonical curve. Math. Ann.206, 157–175 (1963)

    Google Scholar 

  40. Sato, E.: On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties. J. Math. Kyoto Univ.17, 127–150 (1977)

    Google Scholar 

  41. Sato, E.: The decomposability of an infinitely extendable vector bundle on the projective space, II (preprint)

  42. Sato, E.: On infinitely extendable vector bundles onG/P (preprint)

  43. Serre, J.-P.: Sur les modules projectifs. Séminaire Dubreil-Pisot (1960/61), Secr. Math. Paris, exposé 2 (1961)

  44. Takemoto, F.: Stable vector bundles on algebraic surfaces. Nagoya Math. J.47 (1972)

  45. Tango, H.: On morphisms from projective space IPn to the Grassmann varietyGr(n, d) (preprint)

  46. Tyurin, A.N.: Finite dimensional vector bundles over infinite varieties. Math. USSR Isvestija10, 1187–1204 (1976)

    Google Scholar 

  47. Wever, G.P.: The moduli of a class of rank 2 vector bundles on projective 3 space, thesis. Univ. Calif. Berkeley (1977)

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  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Robin Hartshorne

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Partially supported by NSF grant MCS 77-03719

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Hartshorne, R. Stable vector bundles of rank 2 onP 3 . Math. Ann. 238, 229–280 (1978). https://doi.org/10.1007/BF01420250

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