Home Page, Shigeru MUKAI

  • Japanese
    List of publications List of Publications (1995-2003)
    RIMS preprint (2001-2008)
  • #1343: Conterexample to Hilbert's fourteenth problem for the 3-dimensional additive group, 2001
  • #1372: Geometric realization of T-Shaped root systems and counterexamples to Hilbert's fourteenth problem, 2002. (Algebraic Transformation Group and Algebraic Varieties, pp.120-130, Springer Verlag, Berlin, 2004)
  • #1395: Curves and symmetric spaces, II, 2003.
  • #1403: Canonical curves of genus eight, 2003 (with Manabu IDE, Proc. Japan Acad. 79(2003), 59-64)
  • #1422: Plane quartics and Fano threefolds of genus twelve, 2003. (The Fano Conference, pp.563-572, 2004, Univ. Torino)
  • #1502: Finite generation of the Nagata invariant rings in A-D-E cases, 2005.
  • #1505: Counterexample of Kodaira's vanishing and Yau's ineqauality in higher dimensional variety of characteristic p>0, 2005. (Originally typeset around 1980.)
  • #1544: Numerically trivial involutions of Enriques surfaces, May 2006. (One type was omitted in the classification in 1984.)
  • #1562: (with H. Nasu) Obstructions to deforming curves on a 3-fold, I --- a generalization of Mumford's example and an application to Hom schemes ---, July 2006. (To appear in the Journal of Algebraic Geometry.)
  • #1633: Kummer's quartics and numerically reflective involutions of Enriques surfaces, June 2008. (Conjecture 3 has been solved by H. Ohashi in his recent preprint "Enriques surfaces covered by Jacobian Kummer surfaces".)
  • Addendum to #1544: Addendum to "Numerically trivial involutions of Enriques surfaces", October 2009. (Involutions of Lieberman type are not cohomologically trivial.)
    Abstract of my talk at Oberwolfach in September 2009
  • Numerically reflective involutions of Enriques surfaces Oberwolfach09Sep.pdf
    Polarized K3 surfaces of genus 18 and 20, in "Complex projective geometry", Cambridge Univ. Press, 1992, pp. 264--276.
  • Bergen.pdf
    Polarized K3 surfaces of genus thirteen, in "Moduli spaces and arithmetic geometry", Adv. Stud. Pure Math. 45, Math. Soc. Japan, Tokyo, 2006, pp. 315--326.
  • genus13.pdf
    Abstract of my talk at Oberwolfach in June 2006
  • A generalization of Mumford's example (joint work with H. Nasu) owr06.ps owr06.pdf
    Abstracts of my talks at Oberwolfach in July 2004 and in February 2005
  • Finite and infinite generation of Nagata invariant ring Oberwolfach04.ps Oberwolfach04.pdf
  • Geometric proof of finite generation of certain rings of invariants Oberwolfach05.ps Oberwolfach05.pdf
    Vector bundles on a K3 surface
  • math.AG/0304303
    Moduli of abelian surfaces, and regular polyhedral groups (Proc. Workshop "Moduli of Algebraic Varieties and the Monster, Hokkaido Univ., 1999, pp. 68-74.)
  • polyhedral.ps polyhedral.pdf
    Warwick Preprint:1998
  • #13: Abelian variety and spin representation warwick13.ps warwick13.pdf
  • #14: Equations defining a space curve warwick14.ps warwick14.pdf
  • #15: Simple Lie algebras and Legendre variety warwick15.ps warwick15.pdf
    Non-abelian Brill-Noether theory and Fano 3-folds
  • alg-geom/9704015
    Vector bundles and Brill-Noether theory, in "Current Topics in Complex Algebraic Geometry", Cambridge Univ. Press, 1995
  • MSRI.pdf
    Curves and Grassmannians, 1992, Inchoen, Korea (Algebraic Geometry and related Topics, pp.19-40, International Press, 1993, Cambridge, MA)
  • Inchoen.ps Inchoen.pdf
    Problems on characterization of the complex projective space, in `Birational Geometry of Algebraic Varieties, Open Problems, Kataata, 1988' (the 23rd Int'l Symp., Taniguchi Foundation), 1988, pp. 57--60.
  • Taniguchi1988.pdf
    On the moduli spaces of bundles on K3 surfaces, I, "Vector bundles on Algebraic Varieties", Tata Institute of Fundamental Research, Bombay, January, 1984
  • Tata.pdf
    Fourier functor and its application to the moduli of bundles on an abelian variety, in `Algebraic Geometry, Sendai, 1985', Series : Adv. Stud. Pure Math., vol. 10, (T. Oda ed.), 1987, pp. 515-550.
  • Fourier1987.pdf
    (Shigefumi Mori, ---), Classification of Fano 3-folds with B_2 >= 2, I, in `Algebraic and Topological Theories -- to the memory of Dr. Takehiko Miyata', (M. Nagata ed.), Kinokuniya, 1985, pp. 496-545.
  • Fano1985.pdf
    (Shigefumi Mori, ---), On Fano 3-folds with B_2 >= 2, in `Algebraic Varieties and Analytic Varieties', Series : Adv. Stud. Pure Math., vol. 1, (S. Iitaka ed.), 1983, pp. 101-129.
  • Fano1983.pdf
    Errata of "An Introduction to Invariants and Moduli" (Cambridge Univ. Press 2003)

    photo

  • errata.ps errata.pdf

    14) page 24, line 8 The coefficient "3" of the middle term in the right hand side should read "6".

    Last modified: November 11, 2009.