• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
Of all publications in the section: 8
Sort:
by name
by year
Article
Cheltsov I. Journal of Algebraic Geometry. 2010. Vol. 19. P. 781-791.
Added: Dec 6, 2013
Article
Gorchinskiy Sergey, Guletskii V. Journal of Algebraic Geometry. 2012. Vol. 21. No. 2. P. 347-373.

We study links between algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in Q. We decompose the motive of a non-singular projective threefold X with representable algebraic part of CH_0(X) into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the corresponding intermediate Jacobian J^2(X) when the ground field is C. In particular, it implies motivic finite-dimensionality of Fano threefolds over a field. We also prove representability of zero-cycles on several classes of threefolds fibered by surfaces with algebraic H^2. This gives another new examples of three-dimensional varieties whose motives are finite-dimensional.

Added: Feb 5, 2013
Article
Prokhorov Y. Journal of Algebraic Geometry. 2012. Vol. 21. No. 3. P. 563-600.

We classify all finite simple subgroups of the Cremona group Cr3(C).

Added: Sep 19, 2012
Article
Rudakov A. N. Journal of Algebraic Geometry. 1997. Vol. 197. No. 1. P. 231-245.
The main goal of the article is to give the definition of algebraic stability that would permit us to consider stability, not only for algebraic vector bundles or torsion-free coherent sheaves, but for the abelian category of coherent sheaves or for whatever abelian category. We present an axiomatic description of the algebraic stability on an abelian category and prove some general results. Then the stability for coherent sheaves on a projective variety is constructed which generalizes Gieseker stability. Stabilities for graded modules and for quiver representations are also discussed. The constructions could be used for other abelian categories as well.
Added: Oct 16, 2012
Article
Osipov D., Zhu X. Journal of Algebraic Geometry. 2016. Vol. 25. P. 703-774.

We define a two-dimensional Contou-Carrere symbol, which is a deformation of the two-dimensional tame symbol and is a natural generalization of the usual (one-dimensional) Contou-Carrere symbol. We give several constructions of this symbol and investigate its properties. Using higher-categorical methods, we prove reciprocity laws on algebraic surfaces for this symbol. We also relate the two-dimensional Contou-Carrere symbol with the two-dimensional class field theory.

Added: Oct 16, 2017
Article
Y. Prokhorov, Shokurov V. Journal of Algebraic Geometry. 2009. Vol. 18. No. 1. P. 151-199.
Added: Feb 26, 2015
Article
Gritsenko V., Hulek K. Journal of Algebraic Geometry. 2014. Vol. 23. No. 4. P. 711-725.

A strongly reflective modular form with respect to an orthogonal group of signature (2,n) determines a Lorentzian Kac--Moody algebra. We find a new geometric application of such modular forms: we prove that if the weight is larger than n then the corresponding modular variety is uniruled. We also construct new reflective modular forms and thus provide new examples of uniruled moduli spaces of lattice polarised K3 surfaces. Finally we prove that the moduli space of Kummer surfaces associated to (1,21)-polarised abelian surfaces is uniruled.

Added: Feb 26, 2015
Article
Przyjalkowski V., Shramov K., Cheltsov I. Journal of Algebraic Geometry. 2019. Vol. 28. P. 201-243.

We study the rationality problem for nodal quartic double solids. In particular, we prove that nodal quartic double solids with at most six singular points are irrational and nodal quartic double solids with at least eleven singular points are rational.

Added: Jan 26, 2019