Abstract
Here we study the real locus (i.e. the fixed locus by the conjugation) of a few moduli spaces (defined overR) of complex objects (essentially moduli spaces of surfaces of general type or of vector bundles on curves andP 2).
Similar content being viewed by others
References
[A4]Arbarello, E., Cornalba, M., Griffiths, P. A., Harris, J.: Geometry of Algebraic Curves. Vol. I. Berlin, Heidelberg, New York: Springer. 1985.
[B]Ballico, E.: On moduli of vector bundles on rational surfaces. Arch. Math.49, 267–272 (1987).
[BB]Ballico, E., Brusse, R.: On the unbalance of vector bundles on a blown-up surface. Preprint.
[BPS]Banica, C., Putinar, M., Schumacher, G.: Variation der globalen Ext in Deformationen komplexer Räume. Math. Ann.250, 135–155 (1980).
[BFS]Beltrametti, M., Francia, P., Sommese, A.: On Reider's method and higher order embeddings. Duke Math. J.58, 425–439 (1989).
[B1]Brun, J.: Les fibrés de rang deux surP 2 et leurs sections. Bull. Soc. Math. France108, 457–473 (1980).
[C]Catanese, F.: Commutative algebra methods and equations of regular surfaces. In: Algebraic Geometry, Bucharest 1982, pp. 68–111. Lect. Notes Math. 1056 Berlin: Springer. 1984.
[C1]Catanese, F.: On the moduli spaces of surfaces of general type. J. Differential Geom.19, 483–515 (1984).
[C2]Catanese, F.: Equations of pluriregular varieties of general type. In: Geometry of Today, pp. 47–67. Basel: Birkhäuser. 1985.
[C3]Catanese, F.: Footnotes to a theorem of I. Reider. In: Algebraic Geometry, L'Aquila 1988, pp. 67–74. Lect. Notes Math. 1417. Berlin: Springer. 1990.
[CD]Catanese, F., Debarre, O.: Surfaces withK 2=2,p g=1,q=0. J. Reine Angew. Math.395, 1–55 (1989).
[Ch]Chen, Z.: On the geography of surfaces: simply connected minimal surfaces with positive index. Math. Ann.277, 141–164 (1987).
[E]Ellingsrud, G.: Sur l'irréductibilite du module des fibrés stables de rang élevè surP 2. Math. Z.182, 189–192 (1983).
[GH1]Griffiths, P., Harris, J.: Residues and zero-cycles on algebraic varieties. Ann. of Math.127, 309–316.
[GH2]Griffiths, P., Harris, J.: Principle of Algebraic Geometry. New York: Wiley. 1978.
[Ha]Hartshorne, R.: Algebraic Geometry. Berlin: Springer. 1977.
[H]Hirzebruch, F.: Arrangements of lines and algebraic surfaces. In: Progress in Math. 36, pp. 113–140. Basel: Birkhäuser. 1983.
[Hu]Hunt, B.: Complex manifold geography in dimension 2 and 3. J. Differential Geom.30, 51–153 (1989).
[M]Maruyama, M.: Moduli of stable sheaves, II. J. Math. Kyoto Univ.23, 557–614 (1983).
[Mi]Miyaoka, Y.: Algebraic surfaces with positive index. Progress in Math. 39, pp. 281–301. Basel: Birkhäuser. 1983.
[Mu]Mumford, D.: Geometric Invariant Theory. Berlin: Sprigner. 1965.
[P]Persson, U.: Chern invariants of surfaces of general type. Compositio Math.43, 3–58 (1981).
[Se]Seppala, M.: Complex algebraic curves with real moduli. J. Reine Angew. Math.387, 209–220 (1988).
[Si]Silhol, R.: Real Algebraic Surfaces. Lect. Notes Math. 1392. Berlin: Springer. 1989.
[So]Sommese, A.: On the density of ratios of Chern numbers of surfaces of general type. Math. Ann.268, 207–221 (1984).
[X]Xiao, G.: Surfaces fibrées en courbes de genre deux. Lect. Notes Math. 1137. Berlin: Springer. 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ballico, E. Real moduli of complex objects: Surfaces and bundles. Monatshefte für Mathematik 115, 13–26 (1993). https://doi.org/10.1007/BF01311207
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01311207