Tohoku Mathematical Journal

Double lines on quadric hypersurfaces

Edoardo Ballico and Sukmoon Huh

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Abstract

We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 3 (2018), 447-473.

Dates
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1537495356

Digital Object Identifier
doi:10.2748/tmj/1537495356

Mathematical Reviews number (MathSciNet)
MR3856776

Zentralblatt MATH identifier
06996537

Subjects
Primary: 14H10: Families, moduli (algebraic)
Secondary: 14D22: Fine and coarse moduli spaces 14E05: Rational and birational maps

Keywords
pure sheaf locally Cohen-Macaulay curve Hilbert scheme

Citation

Ballico, Edoardo; Huh, Sukmoon. Double lines on quadric hypersurfaces. Tohoku Math. J. (2) 70 (2018), no. 3, 447--473. doi:10.2748/tmj/1537495356. https://projecteuclid.org/euclid.tmj/1537495356


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References

  • E. Arbarello, M. Cornalba and P. A. Griffiths, Geometry of algebraic curves Vol. II with a contribution by J. Harris. Springer-Verlag, 2011.
  • M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452.
  • C. Bănică and O. Forster, Multiplicity structures on space curves, The Lefschetz centennial conference, Part I (Mexico City, 1984), Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1986, pp. 47–64.
  • C. Bănică, Sur les Ext-globaux dans une déformation, Compositio Math. 44 (1981), no. 1-3, 17–27.
  • D. Bayer and D. Eisenbud, Ribbons and their canonical embeddings, Trans. Amer. Math. Soc. 347 (1995), no. 3, 719–756.
  • J. Choi, K. Chung and M. Maican, Moduli of sheaves supported on quartic space curves, Michigan Math. J. 65 (2016), no. 3, 637–671.
  • D. Eisenbud and M. Green, Clifford indices of ribbons}, Trans. Amer. Math. Soc. 347 (1995), no. 3, 757–765.
  • H. G. Freiermuth and G. Trautmann, On the moduli scheme of stable sheaves supported on cubic space curves, Amer. J. Math. 126 (2004), no. 2, 363–393.
  • R. Hartshorne, Algebraic geometry}, Springer-Verlag, New York-Heidelberg, 1977, Graduate Texts in Mathematics, No. 52.
  • R. Hartshorne, The genus of space curves}, Ann. Univ. Ferrara Sez. VII (N.S.) 40 (1994), 207–223 (1996).
  • R. Hartshorne and E. Schlesinger, Curves in the double plane. Special issue in honor of Robin Hartshorne, Comm. Algebra 28 (2000), no. 12, 5655–5676.
  • M. He, Espaces de modules de systèmes cohérents, Internat. J. Math. 9 (1998), no. 5, 545–598.
  • D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, second ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010.
  • J. Le Potier, Faisceaux semi-stables de dimension 1 sur le plan projectif, Rev. Roumaine Math. Pures Appl. 38 (1993), no. 7-8, 635–678.
  • U. Nagel, R. Notari and M. L. Spreafico, The Hilbert scheme of degree two curves and certain ropes, Internat. J. Math. 17 (2006), no. 7, 835–867.
  • R. Piene and M. Schlessinger, On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107 (1985), no. 4, 761–774.
  • C. T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I, Inst. Hautes Études Sci. Publ. Math. (1994), no. 79, 47–129.