Journal of Differential Geometry

Koszul cohomology and the geometry of projective varieties

Mark L. Green

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 19, Number 1 (1984), 125-171.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214438426

Digital Object Identifier
doi:10.4310/jdg/1214438426

Mathematical Reviews number (MathSciNet)
MR739785

Zentralblatt MATH identifier
0559.14008

Subjects
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]

Citation

Green, Mark L. Koszul cohomology and the geometry of projective varieties. J. Differential Geom. 19 (1984), no. 1, 125--171. doi:10.4310/jdg/1214438426. https://projecteuclid.org/euclid.jdg/1214438426


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References

  • [1] E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Special divisors on algebraic curves, to appear.
  • [2] E. Arbarello and E. Semesi, Petri's approach to the ideal associated to a special divisor, Invent. Math. 49 (1978) 99-119.
  • [3] J. Carlson and P. A. Griffiths, Infinitesimal variations of Hodge structures and the global Torelli problem, Jourees de geometrie algebriques d'Angers, Sijthoff and Nordhoff, 1980, 51-76.
  • [4] R. Donagi, Generic Torelli for projective hypersurfaces, to appear.
  • [5] M. L. Green, The canonical ring of a variety of general type, Duke Math. J. 49 (1982) 1087-1113.
  • [6] M. L. Green, The period map for hypersurfaces of high degree on an arbitrary variety, to appear.
  • [7] P. A. Griffiths, Infinitesimal variations of Hodge structure. III, Compositio Math., to appear.
  • [8] P. A. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978.
  • [9] D. Gieseker, Stable curves and special divisors: Petrov's Conjecture, Invent. Math. 66 (1982) 251-275.
  • [10] K. Kii, The local Torelli theorem for varieties with divisible canonical class, Math. USSR-Izv. 12 (1978) 53-67.
  • [11] D. Mumford, Varieties defined by quadratic equations, C. I. M. E. Conference on Questions on Algebraic Varieties, 1969, 31-100.
  • [12] F. Schreyer, Thesis, Brandeis University, to appear.
  • [13] E. Sernesi, L'unirazionalita della varieta dei moduli delle curve di genere dodici, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981) 405-439.

See also

  • Part II: Mark L. Green. Koszul cohomology and the geometry of projective varieties. II. J. Differential Geom., Volume 20, Number 1, (1984), 279--289.