On $L^ 2$-plurigenera of not-log-canonical Gorenstein isolated singularities
HTML articles powered by AMS MathViewer
- by Masataka Tomari and Kimio Watanabe PDF
- Proc. Amer. Math. Soc. 109 (1990), 931-935 Request permission
Abstract:
We will give an application of S. Izumi’s theorems of order functions of analytic spaces to classification problems of isolated singularities by means of plurigenus ${\delta _m}$.References
- Shiro Goto and Keiichi Watanabe, On graded rings. I, J. Math. Soc. Japan 30 (1978), no. 2, 179–213. MR 494707, DOI 10.2969/jmsj/03020179
- Shihoko Ishii, On isolated Gorenstein singularities, Math. Ann. 270 (1985), no. 4, 541–554. MR 776171, DOI 10.1007/BF01455303 —, Isolated ${\mathbf {Q}}$-Gorenstein singularities of dimension three, Adv. Stud. Pure Math. 8 (1986), 165-198.
- Shihoko Ishii, Small deformations of normal singularities, Math. Ann. 275 (1986), no. 1, 139–148. MR 849059, DOI 10.1007/BF01458588 —, The asymptotic behavior of the growth of plurigenera for a normal isolated singularity, Math. Ann. (to appear).
- Shuzo Izumi, Linear complementary inequalities for orders of germs of analytic functions, Invent. Math. 65 (1981/82), no. 3, 459–471. MR 643564, DOI 10.1007/BF01396630
- Shuzo Izumi, A measure of integrity for local analytic algebras, Publ. Res. Inst. Math. Sci. 21 (1985), no. 4, 719–735. MR 817161, DOI 10.2977/prims/1195178926
- Shuzo Izumi, Gabrielov’s rank condition is equivalent to an inequality of reduced orders, Math. Ann. 276 (1986), no. 1, 81–89. MR 863708, DOI 10.1007/BF01450926
- Shuzo Izumi, The rank condition and convergence of formal functions, Duke Math. J. 59 (1989), no. 1, 241–264. MR 1016886, DOI 10.1215/S0012-7094-89-05908-5
- Yujiro Kawamata, Crepant blowing-up of $3$-dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math. (2) 127 (1988), no. 1, 93–163. MR 924674, DOI 10.2307/1971417 D. T. Lê, Algebraic methods in the study of singularities, Lecture Notes Tokyo University Komaba, 1977. M. Lejeune-Jalabert and B. Teisser, Cloture intégrale des ideaux et equisingularite, preprint, Ecole Polytechnique, 1974.
- Marcel Morales, Resolution of quasihomogeneous singularities and plurigenera, Compositio Math. 64 (1987), no. 3, 311–327. MR 918415 D. Rees, Izumi’s theorem, preprint, 1985.
- M. Hochster, C. Huneke, and J. D. Sally (eds.), Commutative algebra, Mathematical Sciences Research Institute Publications, vol. 15, Springer-Verlag, New York, 1989. MR 1015509, DOI 10.1007/978-1-4612-3660-3
- F. Sakai, Kodaira dimensions of complements of divisors, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 239–257. MR 0590433
- Kimio Watanabe, On plurigenera of normal isolated singularities. I, Math. Ann. 250 (1980), no. 1, 65–94. MR 581632, DOI 10.1007/BF01422185
- Kimio Watanabe, On plurigenera of normal isolated singularities. II, Complex analytic singularities, Adv. Stud. Pure Math., vol. 8, North-Holland, Amsterdam, 1987, pp. 671–685. MR 894312, DOI 10.2969/aspm/00810671
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 931-935
- MSC: Primary 32S45
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021213-8
- MathSciNet review: 1021213