Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Type II unprojection

Author: Stavros Argyrios Papadakis
Journal: J. Algebraic Geom. 15 (2006), 399-414
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.

References [Enhancements On Off] (What's this?)

  • [Al] Altinok 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] Altinok 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 MR 1941620 (2004c:14077)
  • [BH] Bruns W. and Herzog J., Cohen-Macaulay rings. Revised edition, Cambridge Studies in Advanced Mathematics 39, CUP 1998 MR 1251956 (95h:13020)
  • [BV] Bruns W. and Vetter U., Determinantal rings. Lecture Notes in Math. 1327, Springer 1988 MR 0953963 (89i:13001)
  • [BS] Buckley A. and Szendroi B., Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry, J. Algebraic Geom. 14 (2005), 601-622 MR 2147356
  • [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 MR 0749939 (86c:14027)
  • [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 MR 1954062 (2003m:14076)
  • [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] Kustin A. and Miller M., Constructing big Gorenstein ideals from small ones. J. Algebra 85 (1983), 303-322 MR 0725084 (85f:13014)
  • [P] Papadakis S., Kustin-Miller unprojection with complexes, J. Algebraic Geometry 13 (2004), 249-268 MR 2047698 (2005d:13025)
  • [P2] Papadakis S., The relations of type II unprojection, work in progress
  • [P3] Papadakis S., Remarks on type III unprojection, math.AG/0501535, to appear in Commun. in Algebra, 11 pp.
  • [PR] Papadakis S. and Reid M., Kustin-Miller unprojection without complexes, J. Algebraic Geometry 13 (2004), 563-577 MR 2047681 (2005j:14068)
  • [R] Reid M., Examples of type IV unprojection, math.AG/0108037, 16 pp.
  • [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.

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

Received by editor(s): August 10, 2004
Received by editor(s) in revised form: July 2, 2005
Published electronically: February 27, 2006

American Mathematical Society