A finiteness theorem for elliptic Calabi-Yau threefolds

previous :: next

A finiteness theorem for elliptic Calabi-Yau threefolds

Mark Gross

Source: Duke Math. J. Volume 74, Number 2 (1994), 271-299.

First Page: Show

Primary Subjects: 14J32

Secondary Subjects: 14J15

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288202
Mathematical Reviews number (MathSciNet): MR1272978
Zentralblatt MATH identifier: 0838.14033
Digital Object Identifier: doi:10.1215/S0012-7094-94-07414-0

back to Table of Contents

References

[1] P. Deligne, Courbes elliptiques: formulaire d'après J. Tate, Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1975, 53–73. Lecture Notes in Math., Vol. 476.

Mathematical Reviews (MathSciNet): MR52:8135

[2] P. Deligne, J.-F. Boutot, L. Illusie, and J.-L. Verdier, Cohomologie Étale, Lecture Notes in Math., vol. 569, Springer-Verlag, Berlin, 1977.

Mathematical Reviews (MathSciNet): MR57:3132

Zentralblatt MATH: 0345.00010

[3] I. Dolgachev and M. Gross, Elliptic threefolds. I. Ogg-Shafarevich theory, J. Algebraic Geom. 3 (1994), no. 1, 39–80.

Mathematical Reviews (MathSciNet): MR95d:14037

Zentralblatt MATH: 0803.14021

[4] A. Grassi, On minimal models of elliptic threefolds, Math. Ann. 290 (1991), no. 2, 287–301.

Mathematical Reviews (MathSciNet): MR92f:14013

Zentralblatt MATH: 0719.14006

Digital Object Identifier: doi:10.1007/BF01459246

[5] A. Grassi, The singularities of the parameter surface of a minimal elliptic threefold, Internat. J. Math. 4 (1993), no. 2, 203–230.

Mathematical Reviews (MathSciNet): MR94h:14036

Zentralblatt MATH: 0802.14020

Digital Object Identifier: doi:10.1142/S0129167X93000121

[6] A. Grassi, Log contractions and equidimensional models of elliptic threefolds, MSRI preprint #055-93, 1993.

Mathematical Reviews (MathSciNet): MR1311349

Zentralblatt MATH: 0840.14026

[7] M. Gross, Elliptic three-folds II: Multiple fibres, MSRI preprint #018-93, 1992.

Mathematical Reviews (MathSciNet): MR1401771

Zentralblatt MATH: 0884.14017

Digital Object Identifier: doi:10.1090/S0002-9947-97-01845-X

JSTOR: links.jstor.org

[8]¹ A. Grothendieck, Le groupe de Brauer. I. Algèbres d'Azumaya et interprétations diverses, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 1968, pp. 46–66.

Mathematical Reviews (MathSciNet): MR39:5586a

Zentralblatt MATH: 0193.21503

[8]² A. Grothendieck, Le groupe de Brauer. II. Théorie cohomologique, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 1968, pp. 67–87.

Mathematical Reviews (MathSciNet): MR39:5586b

Zentralblatt MATH: 0198.25803

[8]³ A. Grothendieck, Le groupe de Brauer. III. Exemples et compléments, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, 1968, pp. 88–188.

Mathematical Reviews (MathSciNet): MR39:5586c

Zentralblatt MATH: 0198.25901

[9] A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique, I, Gtundlehren Math. Wiss., vol. 166, Springer-Verlag, Berlin, 1971.

Zentralblatt MATH: 0203.23301

[10] B. Hunt, A bound on the Euler number for certain Calabi-Yau $3$-folds, J. Reine Angew. Math. 411 (1990), 137–170.

Mathematical Reviews (MathSciNet): MR91j:14033

Zentralblatt MATH: 0745.14016

Digital Object Identifier: doi:10.1515/crll.1990.411.137

[11] Y. Kawamata, Kodaira dimension of certain algebraic fiber spaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1983), no. 1, 1–24.

Mathematical Reviews (MathSciNet): MR84g:14008

Zentralblatt MATH: 0516.14026

[12] J. Kollár and S. Mori, Classification of three-dimensional flips, J. Amer. Math. Soc. 5 (1992), no. 3, 533–703.

Mathematical Reviews (MathSciNet): MR93i:14015

Zentralblatt MATH: 0773.14004

Digital Object Identifier: doi:10.2307/2152704

JSTOR: links.jstor.org

[13] J. Kollàr, et al., Flips and abundance for algebraic threefolds, to appear.

[14] J. S. Milne, Étale cohomology, Princeton Mathematical Series, vol. 33, Princeton University Press, Princeton, N.J., 1980.

Mathematical Reviews (MathSciNet): MR81j:14002

Zentralblatt MATH: 0433.14012

[15] R. Miranda, Smooth models for elliptic threefolds, The birational geometry of degenerations (Cambridge, Mass., 1981), Progr. Math., vol. 29, Birkhäuser Boston, Mass., 1983, pp. 85–133.

Mathematical Reviews (MathSciNet): MR84f:14024

Zentralblatt MATH: 0583.14014

[16] R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z. 193 (1986), no. 4, 537–558.

Mathematical Reviews (MathSciNet): MR88a:14044

Zentralblatt MATH: 0652.14003

Digital Object Identifier: doi:10.1007/BF01160474

[17] M. Miyanishi and D.-Q. Zhang, Gorenstein log del Pezzo surfaces of rank one, J. Algebra 118 (1988), no. 1, 63–84.

Mathematical Reviews (MathSciNet): MR89i:14033

Zentralblatt MATH: 0664.14019

Digital Object Identifier: doi:10.1016/0021-8693(88)90048-8

[18] D. Mumford and K. Suominen, Introduction to the theory of muldi, Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math.), Wolters-Noordhoff, Groningen, 1972, pp. 171–222.

Mathematical Reviews (MathSciNet): MR55:10455

Zentralblatt MATH: 0242.14004

[19] N. Nakayama, On Weierstrass models, Algebraic geometry and commutative algebra, Vol. II, Kinokuniya, Tokyo, 1988, pp. 405–431.

Mathematical Reviews (MathSciNet): MR90m:14030

Zentralblatt MATH: 0699.14049

[20] N. Nakayama, Local structure of an elliptic fibration, preprint, Univ. of Tokyo, 1991.

Mathematical Reviews (MathSciNet): MR1929795

Zentralblatt MATH: 1059.14015

[21] K. Oguiso, On algebraic fiber space structures on a Calabi-Yau threefold, preprint, 1992.

[22] F. Sakai, The structure of normal surfaces, Duke Math. J. 52 (1985), no. 3, 627–648.

Mathematical Reviews (MathSciNet): MR87k:14038

Zentralblatt MATH: 0699.14049

Digital Object Identifier: doi:10.1215/S0012-7094-85-05233-0

Project Euclid: euclid.dmj/1077304585

[23] C. Schoen, On fiber products of rational elliptic surfaces with section, Math. Z. 197 (1988), no. 2, 177–199.

Mathematical Reviews (MathSciNet): MR89c:14062

Zentralblatt MATH: 0631.14032

Digital Object Identifier: doi:10.1007/BF01215188

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?