The Michigan Mathematical Journal

Extensions of two Chow stability criteria to positive characteristics

Shinnosuke Okawa

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 60, Issue 3 (2011), 687-703.

Dates
First available in Project Euclid: 8 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1320763055

Digital Object Identifier
doi:10.1307/mmj/1320763055

Mathematical Reviews number (MathSciNet)
MR2861095

Zentralblatt MATH identifier
1230.14068

Subjects
Primary: 14L24: Geometric invariant theory [See also 13A50]
Secondary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24] 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Okawa, Shinnosuke. Extensions of two Chow stability criteria to positive characteristics. Michigan Math. J. 60 (2011), no. 3, 687--703. doi:10.1307/mmj/1320763055. https://projecteuclid.org/euclid.mmj/1320763055


Export citation

References

  • I. Dolgachev, Lectures on invariant theory, London Math. Soc. Lecture Note Ser., 296, Cambridge Univ. Press, Cambridge, 2003.
  • I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Math. Theory Appl., Birkhäuser, Boston, 1994.
  • A. Grothendieck, Éléments de géométrie algébrique IV, Étude locale des schémas et des morphismes de schémas III, Inst. Hautes Études Sci. Publ. Math. 28 (1966).
  • N. Hara and K.-I. Watanabe, F-regular and F-pure rings vs. log terminal and log canonical singularities, J. Algebraic Geom. 11 (2002), 363–392.
  • R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York, 1977.
  • H. Kim and Y. Lee, Log canonical thresholds of semistable plane curves, Math. Proc. Cambridge Philos. Soc. 137 (2004), 273–280.
  • J. Kollár, Rational curves on algebraic varieties, Ergeb. Math. Grenzgeb. (3), 32, Springer-Verlag, Berlin, 1996.
  • –––, Singularities of pairs, Algebraic geometry (Santa Cruz, 1995), Proc. Sympos. Pure Math., 62, pp. 221–287, Amer. Math. Soc., Providence, RI, 1997.
  • J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998.
  • R. Laza, The moduli space of cubic fourfolds, J. Algebraic Geom. 18 (2009), 511–545.
  • R. Lazarsfeld, Positivity in algebraic geometry II, Ergeb. Math. Grenzgeb. (3), 48, Springer-Verlag, Berlin, 2004.
  • Y. Lee, Chow stability criterion in terms of log canonical threshold, J. Korean Math. Soc. 45 (2008), 467–477.
  • H. Matsumura, Commutative algebra, 2nd ed., Math. Lecture Note Ser., 56, Benjamin/Cummings, Reading, MA, 1980.
  • H. Matsumura and P. Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (1963/64), 347–361.
  • S. Mukai, An introduction to invariants and moduli, Cambridge Stud. Adv. Math., 81, Cambridge Univ. Press, Cambridge, 2003.
  • D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 3rd ed., Ergeb. Math. Grenzgeb. (2), 34, Springer-Verlag, Berlin, 1994.
  • M. Mustaţă, Singularities of pairs via jet schemes, J. Amer. Math. Soc. 15 (2002), 599–615.
  • L. Ness, Mumford's numerical function and stable projective hypersurfaces, Algebraic geometry (Copenhagen, 1978), Lecture Notes in Math., 732, pp. 417–453, Springer-Verlag, Berlin, 1979.
  • A. N. Rudakov and I. R. Šafarevič, Inseparable morphisms of algebraic surfaces, Math. USSR-Izv. 40 (1976), 1205–1237.
  • J. P. Serre, Local fields, Grad. Texts in Math., 67, Springer-Verlag, New York, 1979.
  • C. S. Seshadri, Geometric reductivity over arbitrary base, Adv. Math. 26 (1977), 225–274.
  • J. Shah, A complete moduli space for $K3$ surfaces of degree 2, Ann. of Math. (2) 112 (1980), 485–510.
  • T. Yasuda, Twisted jets, motivic measures and orbifold cohomology, Compositio Math. 140 (2004), 396–422.