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Tight Closure and Plus Closure for Cones Over Elliptic Curves

Published online by Cambridge University Press:  11 January 2016

Holger Brenner
Holger Brenner*
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom, H.Brenner@sheffield.ac.uk
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Abstract

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We characterize the tight closure of a homogeneous primary ideal in a normal homogeneous coordinate ring over an elliptic curve by a numerical condition and we show that it is in positive characteristic the same as the plus closure.

Keywords

13A3514H6014H5214M2014C20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 177 , 2005 , pp. 31 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[1] Atiyah, M. F., Vector bundles over an elliptic curve, Proc. London Math. Soc., 7 (1957), 414–452.Google Scholar
[2] Beltrametti, M. C. and Sommese, A. J., The Adjunction Theory of Complex Projective Varieties, De Gruyter, Berlin, 1995.Google Scholar
[3] Brenner, H., Tight closure and projective bundles, J. Algebra, 265 (2003), 45–78.Google Scholar
[4] Gieseker, D., p-ample bundles and their chern classes, Nagoya Math. J., 43 (1971), 91–116.Google Scholar
[5] Hartshorne, R., Ample vector bundles on curves, Nagoya Math. J., 43 (1971), 73–89.Google Scholar
[6] Hochster, M., Solid closure, Contemp. Math., 159 (1994), 103–172.Google Scholar
[7] Hochster, M. and Huneke, C., Tight closure of parameter ideals and splittings in module finite extensions, J. Alg. Geom., 3 (1994), 599–670.Google Scholar
[8] Huneke, C., Tight Closure, Parameter Ideals, and Geometry, Six Lectures on Commutative Algebra, Birkhäuser, Basel (1998).Google Scholar
[9] MacLane, S., Homology, Springer, Berlin, 1967.Google Scholar
[10] McDermott, M. A., Tight closure, plus closure and Frobenius closure in cubical cones, Trans. Am. Math. Soc., 352 (2000), no. 1, 95–114.Google Scholar
[11] Miyaoka, Y., The Chern class and Kodaira dimension of a minimal variety, Algebraic Geometry, Sendai 1985, Adv. Stud. Pure Math., 10 (1987), 449–476.Google Scholar
[12] Mumford, D., Abelian Varieties, Oxford University Press, Bombay, 1970.Google Scholar
[13] Oda, T., Vector bundles on an elliptic curve, Nagoya Math. J., 43 (1971), 41–72.Google Scholar
[14] Silverman, J. H., The Arithmetic of Elliptic Curves, Springer, Berlin, 1986.Google Scholar
[15] Singh, A., A computation of tight closure in diagonal hypersurfaces, J. Algebra, 203 (1998), no. 2, 579–589.Google Scholar
[16] Smith, K. E., Tight closure of parameter ideals, Inventiones Math., 115 (1994), 41–60.Google Scholar