Illinois Journal of Mathematics

Characterizations of projective hulls by analytic discs

Barbara Drinovec Drnovšek and Franc Forstnerič

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The notion of the projective hull of a compact set in a complex projective space $\mathbb{P}^{n}$ was introduced by Harvey and Lawson in 2006. In this paper, we describe the projective hull by Poletsky sequences of analytic discs, in analogy to the known descriptions of the holomorphic and the plurisubharmonic hull.

Article information

Source
Illinois J. Math. Volume 56, Number 1 (2012), 53-65.

Dates
First available in Project Euclid: 27 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1380287459

Mathematical Reviews number (MathSciNet)
MR3117017

Zentralblatt MATH identifier
1311.32013

Subjects
Primary: 32U05: Plurisubharmonic functions and generalizations [See also 31C10]
Secondary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 32E10: Stein spaces, Stein manifolds

Citation

Drinovec Drnovšek, Barbara; Forstnerič, Franc. Characterizations of projective hulls by analytic discs. Illinois J. Math. 56 (2012), no. 1, 53--65. https://projecteuclid.org/euclid.ijm/1380287459.


Export citation

References

  • H. Alexander and J. Wermer, Polynomial hulls with convex fibers, Math. Ann. 271 (1985), 99–109.
  • E. Bedford and B. A. Taylor, Plurisubharmonic functions with logarithmic singularities, Ann. Inst. Fourier (Grenoble) 38 (1988), 133–171.
  • M. Colţoiu, Complete locally pluripolar sets, J. Reine Angew. Math. 412 (1990), 108–112.
  • J.-P. Demailly, Cohomology of $q$-convex spaces in top degrees, Math. Z. 204 (1990), 283–295.
  • B. Drinovec Drnovšek and F. Forstnerič, The Poletsky–Rosay theorem on singular complex spaces, to appear in Indiana Univ. Math. J. 61 (2012); available at http://arxiv.org/abs/1104.3968.
  • B. Drinovec Drnovšek and F. Forstnerič, Disc functionals and Siciak–Zaharyuta extremal functionson singular varieties, Ann. Polon. Math. 106 (2012), 171–191.
  • J. Duval and N. Sibony, Polynomial convexity, rational convexity, and currents, Duke Math. J. 79 (1995), 487–513.
  • F. Forstnerič, Stein manifolds and holomorphic mappings (the homotopy principle in complex analysis), Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, vol. 56, Springer, Berlin, 2011.
  • V. Guedj and A. Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005), 607–639.
  • F. R. Harvey and H. B. Lawson, Jr., Projective hulls and the projective Gelfand transform, Asian J. Math. 10 (2006), 607–646.
  • M. Klimek, Pluripotential theory, London Math. Soc. Monographs, New Series, vol. 6, The Clarendon Press, Oxford University Press, New York, 1991.
  • F. Lárusson and R. Sigurdsson, The Siciak–Zaharyuta extremal function as the envelope of disc functionals, Ann. Polon. Math. 86 (2005), 177–192.
  • H. B. Lawson, Jr. and J. Wermer, Analytic disks and the projective hull, preprint.
  • E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85–144.
  • J.-P. Rosay, Poletsky theory of disks on holomorphic manifolds, Indiana Univ. Math. J. 52 (2003), 157–169.
  • J.-P. Rosay, Approximation of non-holomorphic maps, and Poletsky theory of discs, J. Korean Math. Soc. 40 (2003), 423–434.
  • J. Wermer, The hull of a curve in $\C^n$, Ann. of Math. (2) 68 (1958), 550–561.
  • E. F. Wold, A note on polynomial convexity: Poletsky discs, Jensen measures and positive currents, J. Geom. Anal. 21 (2010), 252–255.