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]**Altinok S.,*Graded rings corresponding to polarised K3 surfaces and -Fano 3-folds*. Univ. of Warwick Ph.D. thesis, Sept. 1998, 93+ vii pp.**[ABR]**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**, https://doi.org/10.1090/conm/314/05420**[BH]**Winfried Bruns and Jürgen Herzog,*Cohen-Macaulay rings*, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR**1251956****[BV]**Bruns W. and Vetter U.,*Determinantal rings*. Lecture Notes in Math. 1327, Springer 1988 MR**0953963 (89i:13001)****[BS]**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**, https://doi.org/10.1090/S1056-3911-05-00403-0**[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]**Alessio Corti and Miles Reid,*Weighted Grassmannians*, Algebraic geometry, de Gruyter, Berlin, 2002, pp. 141–163. MR**1954062****[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]**Stavros Argyrios Papadakis,*Kustin-Miller unprojection with complexes*, J. Algebraic Geom.**13**(2004), no. 2, 249–268. MR**2047698**, https://doi.org/10.1090/S1056-3911-03-00350-3**[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]**Stavros Argyrios Papadakis and Miles Reid,*Kustin-Miller unprojection without complexes*, J. Algebraic Geom.**13**(2004), no. 3, 563–577. MR**2047681**, https://doi.org/10.1090/S1056-3911-04-00343-1**[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. 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

DOI:
https://doi.org/10.1090/S1056-3911-06-00433-4

Received by editor(s):
August 10, 2004

Received by editor(s) in revised form:
July 2, 2005

Published electronically:
February 27, 2006