Advanced search
Publication Cover
Communications in Algebra Volume 50, 2022 - Issue 9
Submit an article Journal homepage
53
Views
2
CrossRef citations to date
0
Altmetric
Articles

Ample stable vector bundles on rational surfaces

Jack HuizengaDepartment of Mathematics, The Pennsylvania State University, University Park, Pennsylvania, USAORCID Iconhttps://orcid.org/0000-0002-5562-0878View further author information
ORCID Icon &
John KopperDepartment of Mathematics, The Pennsylvania State University, University Park, Pennsylvania, USACorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-4279-0800View further author information
ORCID Icon
Pages 3744-3760 | Received 01 Dec 2021, Accepted 08 Feb 2022, Published online: 14 Mar 2022

References

  • Ballico, E., Lanteri, A. (1991). Ample and spanned vector bundles with c2=2 on complex surfaces. Arch. Math. (Basel). 56(6):611–615.
  • Beauville, A. (1983). Complex Algebraic Surfaces. London Mathematical Society Lecture Note Series. Vol. 68. Cambridge: Cambridge University Press.
  • Bertram, A., Goller, T., Johnson, D. (2016). Le Potier’s strange duality, Quot schemes, and multiple point formulas for del Pezzo surfaces. arXiv:1610.04185.
  • Coskun, I., Huizenga, J. (2021). Existence of semistable sheaves on Hirzebruch surfaces. Adv. Math. 381(1):107636. DOI: 10.1016/j.aim.2021.107636.
  • Coskun, I., Huizenga, J. (2020). Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces. Nagoya Math. J. 238:1–36. DOI: 10.1017/nmj.2018.17.
  • Drézet, J.-M., Le Potier, J. (1985). Fibrés stables et fibrés exceptionnels sur P2. Ann. Sci. École Norm. Sup. 18(2):193–243. DOI: 10.24033/asens.1489.
  • Göttsche, L., Hirschowitz, A. (1998). Weak Brill-Noether for vector bundles on the projective plane. In: Algebraic Geometry (Catania, 1993/Barcelona, 1994). Lecture Notes in Pure and Applied Mathematics, Vol. 200. New York: Dekker, pp. 63–74.
  • Fulton, W. (1976). Ample vector bundles, Chern classes, and numerical criteria. Invent. Math. 32(2):171–178. DOI: 10.1007/BF01389960.
  • Fulton, W., Lazarsfeld, R. (1983). Positive polynomials for ample vector bundles. Ann. Math. (2). 118(1):35–60. DOI: 10.2307/2006953.
  • Gieseker, D. (1971). p-ample bundles and their Chern classes. Nagoya Math. J. 43:91–116. DOI: 10.1017/S0027763000014380.
  • Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Mathematics, Vol. 52. New York: Springer-Verlag.
  • Hirschowitz, A., Laszlo, Y. (1993). Fibrés génériques sur le plan projectif. Math. Ann. 297(1):85–102. DOI: 10.1007/BF01459489.
  • Huizenga, J. (2015). Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles. J. Algebraic Geom. 25(1):19–75. DOI: 10.1090/jag/652.
  • Huybrechts, D., Lehn, M. (2010). The Geometry of Moduli Spaces of Sheaves. Cambridge Mathematical Library, 2nd ed. Cambridge: Cambridge University Press.
  • Lazarsfeld, R. (2004). Positivity in Algebraic Geometry II, Positivity for Vector Bundles, and for Multiplier Ideals. Berlin, Heidelberg: Springer-Verlag.
  • Le Potier, J. (1980). Stabilité et amplitude sur. ℙ2(ℂ). In: Hirschowitz, A., ed. Vector Bundles and Differential Equations. Progress in Mathematics. Boston, USA: Birkhauser.
  • Le Potier, J. (1997). Lectures on Vector Bundles. Cambridge Studies in Advanced Mathematics, Vol. 54. Maciocia, A., trans. Cambridge, UK: Cambridge University Press.
  • Mori, S. (1979). Projective manifolds with ample tangent bundle. Ann. Math. (2). 110(3):593–606. DOI: 10.2307/1971241.
  • O’Grady, K. G. (1996). Moduli of vector bundles on projective surfaces: Some basic results. Invent. Math. 123:141–207.
  • Sterian, A. (2012). Stable ample 2-vector bundles on Hirzebruch surfaces. Bull. Math. Soc. Sci. Math. Roumanie (N.S.). 55(1033):311–317.
  • Walter, C. (1998). Irreducibility of moduli spaces of vector bundles on birationally ruled surfaces. In: Algebraic Geometry (Catania, 1993/Barcelona, 1994). Lecture Notes in Pure and Applied Mathematics. Vol. 200. New York: Dekker, pp. 201–211.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.