A note on the defining equations of singular varieties

Author:
Seunghun Lee

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2535-2541

MSC (2000):
Primary 14F17; Secondary 14C20

DOI:
https://doi.org/10.1090/S0002-9939-02-06478-X

Published electronically:
April 10, 2002

MathSciNet review:
1900859

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the vanishing theorem of Bertram, Ein, and Lazarsfeld also holds for varieties with mild singularities.

**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.**Y. Kawamata*Subadjunction of log canonical divisors II.*, Amer. J. Math.,**120**(1998), pp. 893-899. MR**2000d:14020****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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
14F17,
14C20

Retrieve articles in all journals with MSC (2000): 14F17, 14C20

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:
https://doi.org/10.1090/S0002-9939-02-06478-X

Received by editor(s):
January 17, 2000

Received by editor(s) in revised form:
April 10, 2001

Published electronically:
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

Article copyright:
© Copyright 2002
American Mathematical Society