Tohoku Mathematical Journal

Distribution formula for terminal singularities on the minimal resolution of a quasi-homogeneous simple $K3$ singularity

Kimio Watanabe

Article information

Source
Tohoku Math. J. (2), Volume 43, Number 2 (1991), 275-288.

Dates
First available in Project Euclid: 3 May 2007

https://projecteuclid.org/euclid.tmj/1178227498

Digital Object Identifier
doi:10.2748/tmj/1178227498

Mathematical Reviews number (MathSciNet)
MR1104433

Zentralblatt MATH identifier
0760.14003

Citation

Watanabe, Kimio. Distribution formula for terminal singularities on the minimal resolution of a quasi-homogeneous simple $K3$ singularity. Tohoku Math. J. (2) 43 (1991), no. 2, 275--288. doi:10.2748/tmj/1178227498. https://projecteuclid.org/euclid.tmj/1178227498

References

• [F] A R FLETCHER, Plurigenera of 3-folds and weighted hypersurfaces, Thesis submitted for the degree of Doctor of Philosophy at the University of Warwick, 1988.
• [11] S ISHII, On isolated Gorenstein singularities, Math Ann. 270 (1985), 541-554
• [12] S ISHII, Two-dimensional singularities with bounded plurigenera m are -Gorenstein singularities, Contemporary Math. 90 (1989), 135-145.
• [K] Y. KAWAMATA, On the plurigenera of minimalalgebraic 3-Folds with K 0, Math Ann 275 (1986), 539-546
• [KMM] Y. KAWAMATA, K MATSUDA AND K. MATSUKI, Minimal model problem, in Algebraic Geometry, Sendai, 1985 (T Oda, ed), Advanced Studies in Pure Math 10, Kinokuniya, Tokyo and North-Holland, Amsterdam, New York, Oxford, 1987, 283-360
• [KT] R KOBAYASHI AND A. N. ToDOROV, Polarized period map for generalized K3 surfaces and th moduli of Einstein metrics, Thoku Math. J 39 (1987), 341-363.
• [M] S MORI, Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math Soc (1988), 117-253
• [Rl] M. REID, Canonical 3-folds, Journees de Geometric Algebrique d'Angers (A. Beauville, ed), Sijthof and Noordhoff, Alphen aan den Rijn, 1980, 273-310.
• [R2] M. REID, Minimal model of canonical 3-folds, in Algebraic Varieties and Analytic Varieties (S. litaka, ed.), Advanced Studies in Pure Math 1, Kinokuniya, Tokyo, and North-Holland, Amsterdam, New York, Oxford, 1983, 131-180.
• [S] R. STANLEY, Hubert functions of graded algebras Adv in Math 28, 1978, 57-8
• [T] M TOMARI, On the uniqueness of minimal model of singularities, preprint, 1990
• [U] Y. UMEZU, On normal projective surfaces with trivial dualizing sheaf, Tokyo J. Math. 4 (1981), 343-354
• [Wl] K. WATANABE, On plurigenera of normal isolated singularities, I, Math. Ann 250 (1980), 65-94
• [W2] K WATANABE, On plurigenera of normal isolated singularities, II, in Complex Analytic Singularitie (T. Suwa and P Wagrech, eds), Advanced Studies in Pure Math 8, Kinokuniya, Tokyo and North-Holland, Amsterdam, New York, Oxford, 1986, 671-685
• [W3] K. WATANABE, Riemann-Roch theorem for normal isolated singularities, preprint, 1989
• [WI] K. WATANABE AND S. ISHII, On simple K3 singularities (in Japanese), in Proc. of Conf. on Algebrai Geometry at Tokyo Metropolitan Univ., 1988 (N. Sasakura, ed.), 20-31
• [W] K WATANABE AND T. YONEMURA, On ring-theoretic genus r and plurigenera m of norma isolated singularities, preprint, 1988
• [Y] T. YONEMURA, Hypersurface simple K3 singularities, Thoku Math J 42 (1990), 351-380