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A note on the defining equations of singular varieties
Author(s):
Seunghun
Lee
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2535-2541.
MSC (2000):
Primary 14F17;
Secondary 14C20
Posted:
April 10, 2002
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Abstract:
We show that the vanishing theorem of Bertram, Ein, and Lazarsfeld also holds for varieties with mild singularities.
References:
-
- 1.
- M. Artin, On isolated rational singularities of surfaces, Amer. J. Math., 88 (1966), pp. 129-136. MR 33:7340
- 2.
- A. Bertram An application of a log version of the Kodaira vanishing theorem to embedded projective varieties, alg-geom/9707001.
- 3.
- A. Bertram, L. Ein and R. Lazarsfeld Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J.Amer.Math.Soc., 4 (1991), pp. 587-602. MR 92g:14014
- 4.
- L. Ein, Multiplier ideals, Vanishing theorem and Applications Proc. Sympos. Pure. Math. Part1. 62, Amer. Math. Soc., Providence, RI, (1997) pp.203-219. MR 98m:14006
- 5.
- Y. Kawamata Crepant blowing-up of
 -dimensional canonical singularities and its application to degenerations of surfaces, Ann. of Math., 127 (1988), pp. 93-163. MR 89d:14023 - 6.
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- 7.
- Y. Kawamata, K. Matsuda, K. Matsuki Introduction to the minimal model problem Adv. Stud. Pure. Math., 10, North-Holland, Amsterdam-New York, (1987) pp.283-360. MR 89e:14015
- 8.
- J. Kollár Singularities of Pairs Proc. Sympos. Pure. Math. Part1. 62, Amer. Math. Soc., Providence, RI, (1997) pp.221-287. MR 99m:14033
- 9.
- M. Reid Canonical
 -folds Journées de Géometrie Algébique d'Angers, Sijthoff and Noordhoff, Alphen aan den Rijn, (1980) pp. 273-310. MR 82i:14025
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Additional Information:
Seunghun
Lee
Affiliation:
Max-Planck-Institut für Mathematik Vivatsgasse 7, D-53111 Bonn, Germany
Address at time of publication:
Department of Mathematics, Konkuk University, Kwangjin-Gu Hwayang-dong 1, Seoul 143-701, Korea
Email:
mbrs@kkucc.konkuk.ac.kr
DOI:
10.1090/S0002-9939-02-06478-X
PII:
S 0002-9939(02)06478-X
Received by editor(s):
January 17, 2000
Received by editor(s) in revised form:
April 10, 2001
Posted:
April 10, 2002
Additional Notes:
The work was supported by grant No. R01-1999-00004 from the Korea Science and Engineering Foundation.
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2002,
American Mathematical Society
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