On the decomposition of the small diagonal of a K3 surface
-
Ivan Bazhov
Abstract
We give a new proof of the theorem of Beauville and Voisin about the decomposition of the small diagonal of a K3 surface S. Our proof is explicit and works with the embedding of S in
Communicated by: I. Coskun
References
[1] A. Beauville, C. Voisin, On the Chow ring of a K3 surface. J. Algebraic Geom. 13 (2004), 417-426. MR2047674 Zbl 1069.1400610.1090/S1056-3911-04-00341-8Search in Google Scholar
[2] M. A. A. de Cataldo, L. Migliorini, The Chow groups and the motive of the Hilbert scheme of points on a surface. J. Algebra 251 (2002), 824-848. MR1919155 Zbl 1033.1400410.1006/jabr.2001.9105Search in Google Scholar
[3] L. Fu, Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections. Adv. Math. 244 (2013), 894-924. MR3077892 Zbl 1300.1400710.1016/j.aim.2013.06.008Search in Google Scholar
[4] W. Fulton, Intersection theory. Springer 1998. MR1644323 Zbl 0885.1400210.1007/978-1-4612-1700-8Search in Google Scholar
[5] M. Lehn, Chern classes of tautological sheaves on Hilbert schemes of points on surfaces. Invent. Math. 136 (1999), 157-207. MR1681097 Zbl 0919.1400110.1007/s002220050307Search in Google Scholar
[6] M. Lehn, C. Sorger, The cup product of Hilbert schemes for K3 surfaces. Invent. Math. 152 (2003), 305-329. MR1974889 Zbl 1035.1400110.1007/s00222-002-0270-7Search in Google Scholar
[7] D. Mumford, Rational equivalence of 0-cycles on surfaces. J. Math. Kyoto Univ. 9 (1968), 195-204. MR0249428 Zbl 0184.4660310.1007/978-1-4757-4265-7_28Search in Google Scholar
[8] K. G. O'Grady, Computations with modified diagonals. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25 (2014), 249-274. MR3256208 Zbl 1305.1400210.4171/RLM/677Search in Google Scholar
[9] C. Voisin, Intrinsic pseudo-volume forms and K-correspondences. In: The Fano Conference, 761-792, Univ. Torino, Turin 2004. MR2112602 Zbl 1177.14040Search in Google Scholar
[10] C. Voisin, On the Chow ring of certain algebraic hyper-Kähler manifolds. Pure Appl. Math. Q. 4 (2008), 613-649. MR2435839 Zbl 1165.1401210.4310/PAMQ.2008.v4.n3.a2Search in Google Scholar
[11] C. Voisin, Chow rings and decomposition theorems for families of K3 surfaces and Calabi-Yau hypersurfaces. Geom. Topol. 16 (2012), 433-473. MR2916291 Zbl 1253.1400510.2140/gt.2012.16.433Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
