Type II unprojection
Author:
Stavros Argyrios Papadakis
Journal:
J. Algebraic Geom. 15 (2006), 399-414
DOI:
https://doi.org/10.1090/S1056-3911-06-00433-4
Published electronically:
February 27, 2006
MathSciNet review:
2219843
Full-text PDF
Abstract |
References |
Additional Information
Abstract: Answering a question of M. Reid, we define and prove the Gorensteiness of the type II unprojection.
[Al]Al Altınok S., Graded rings corresponding to polarised K3 surfaces and $\mathbb Q$-Fano 3-folds. Univ. of Warwick Ph.D. thesis, Sept. 1998, 93+ vii pp.
- Selma Altınok, Gavin Brown, and Miles Reid, Fano 3-folds, $K3$ surfaces and graded rings, Topology and geometry: commemorating SISTAG, Contemp. Math., vol. 314, Amer. Math. Soc., Providence, RI, 2002, pp. 25–53. MR 1941620, DOI https://doi.org/10.1090/conm/314/05420
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- Winfried Bruns and Udo Vetter, Determinantal rings, Lecture Notes in Mathematics, vol. 1327, Springer-Verlag, Berlin, 1988. MR 953963
- Anita Buckley and Balázs Szendröi, Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry, J. Algebraic Geom. 14 (2005), no. 4, 601–622. MR 2147356, DOI https://doi.org/10.1090/S1056-3911-05-00403-0
- Fabrizio Catanese, Commutative algebra methods and equations of regular surfaces, Algebraic geometry, Bucharest 1982 (Bucharest, 1982) Lecture Notes in Math., vol. 1056, Springer, Berlin, 1984, pp. 68–111. MR 749939, DOI https://doi.org/10.1007/BFb0071770
- Alessio Corti and Miles Reid, Weighted Grassmannians, Algebraic geometry, de Gruyter, Berlin, 2002, pp. 141–163. MR 1954062
[CPR]CPR Corti A., Pukhlikov A. and Reid M., Birationally rigid Fano hypersurfaces, in Explicit birational geometry of 3-folds, A. Corti and M. Reid (eds.), CUP 2000, 175–258
- Andrew R. Kustin and Matthew Miller, Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983), no. 2, 303–322. MR 725084, DOI https://doi.org/10.1016/0021-8693%2883%2990096-0
- Stavros Argyrios Papadakis, Kustin-Miller unprojection with complexes, J. Algebraic Geom. 13 (2004), no. 2, 249–268. MR 2047698, DOI https://doi.org/10.1090/S1056-3911-03-00350-3
[P2]P2 Papadakis S., The relations of type II unprojection, work in progress
[P3]P3 Papadakis S., Remarks on type III unprojection, math.AG/0501535, to appear in Commun. in Algebra, 11 pp.
- Stavros Argyrios Papadakis and Miles Reid, Kustin-Miller unprojection without complexes, J. Algebraic Geom. 13 (2004), no. 3, 563–577. MR 2047681, DOI https://doi.org/10.1090/S1056-3911-04-00343-1
[R]R Reid M., Examples of type IV unprojection, math.AG/0108037, 16 pp.
[Ki]Ki Reid M., Graded Rings and Birational Geometry, in Proc. of algebraic symposium (Kinosaki, Oct 2000), K. Ohno (Ed.) 1–72, available from www.maths. warwick.ac.uk/ miles/3folds
[Al]Al Altınok S., Graded rings corresponding to polarised K3 surfaces and $\mathbb Q$-Fano 3-folds. Univ. of Warwick Ph.D. thesis, Sept. 1998, 93+ vii pp.
[ABR]ABR Altınok S., Brown G. and Reid M., Fano 3-folds, $K3$ surfaces and graded rings, in Topology and geometry: commemorating SISTAG, Contemp. Math., 314, AMS 2002, 25–53
[BH]BH Bruns W. and Herzog J., Cohen-Macaulay rings. Revised edition, Cambridge Studies in Advanced Mathematics 39, CUP 1998
[BV]BV Bruns W. and Vetter U., Determinantal rings. Lecture Notes in Math. 1327, Springer 1988
[BS]BS Buckley A. and Szendrői B., Orbifold Riemann–Roch for threefolds with an application to Calabi–Yau geometry, J. Algebraic Geom. 14 (2005), 601–622
[Ca]Ca Catanese F., Commutative algebra methods and equations of regular surfaces, in Algebraic geometry, Bucharest 1982, Lecture Notes in Math. 1056, Springer 1984, 68–111
[CR]CR Corti A. and Reid M., Weighted Grassmannians, in Algebraic geometry, A volume in memory of Paolo Francia, M. Beltrametti et al. (eds.), de Gruyter 2002, 141–163
[CPR]CPR Corti A., Pukhlikov A. and Reid M., Birationally rigid Fano hypersurfaces, in Explicit birational geometry of 3-folds, A. Corti and M. Reid (eds.), CUP 2000, 175–258
[KM]KM Kustin A. and Miller M., Constructing big Gorenstein ideals from small ones. J. Algebra 85 (1983), 303–322
[P]P Papadakis S., Kustin–Miller unprojection with complexes, J. Algebraic Geometry 13 (2004), 249-268
[P2]P2 Papadakis S., The relations of type II unprojection, work in progress
[P3]P3 Papadakis S., Remarks on type III unprojection, math.AG/0501535, to appear in Commun. in Algebra, 11 pp.
[PR]PR Papadakis S. and Reid M., Kustin–Miller unprojection without complexes, J. Algebraic Geometry 13 (2004), 563–577
[R]R Reid M., Examples of type IV unprojection, math.AG/0108037, 16 pp.
[Ki]Ki Reid M., Graded Rings and Birational Geometry, in Proc. of algebraic symposium (Kinosaki, Oct 2000), K. Ohno (Ed.) 1–72, available from www.maths. warwick.ac.uk/ miles/3folds
Additional Information
Stavros Argyrios Papadakis
Affiliation:
Mathematik und Informatik, Geb. 27, Universitaet des Saarlandes, D-66123 Saarbruecken, Germany
Address at time of publication:
Department of Mathematics, University of Crete, Knossos Avenue, GR-71409 Heraklion, Greece
Email:
spapad@maths.warwick.ac.uk
Received by editor(s):
August 10, 2004
Received by editor(s) in revised form:
July 2, 2005
Published electronically:
February 27, 2006
