Kernels of numerical pushforwards
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Mihai Fulger
Abstract
Let π : X → Y be a morphism of projective varieties and π∗ :Nk(X) → Nk(Y) the pushforward map of numerical cycle classes. We show that when the Chow groups of points of the fibers are as simple as they can be, then the kernel of π∗ is spanned by k-cycles contracted by π.
Funding
The second author is supported by NSF Award 1004363.
References
[1] S. Bloch, V. Srinivas, Remarks on correspondences and algebraic cycles. Amer. J. Math. 105 (1983), 1235–1253. MR714776 Zbl 0525.1400310.2307/2374341Search in Google Scholar
[2] A. J. de Jong, Smoothness, semi-stability and alterations. Inst. Hautes Études Sci. Publ. Math. no. 83 (1996), 51–93. MR1423020 Zbl 0916.1400510.1007/BF02698644Search in Google Scholar
[3] O. Debarre, Z. Jiang, C. Voisin, Pseudo-effective classes and pushforwards. Pure Appl. Math. Q. 9 (2013), 643–664. MR3263971 Zbl 1319.1401010.4310/PAMQ.2013.v9.n4.a3Search in Google Scholar
[4] M. Fulger, B. Lehmann, Morphisms and faces of pseudo-effective cones. Proc. Lond. Math. Soc. (3) 112 (2016), 651–676. MR3483128 Zbl 1348.1403910.1112/plms/pdw008Search in Google Scholar
[5] M. Fulger, B. Lehmann, Positive cones of dual cycle classes. 2014, to appear in Alg. Geom.Search in Google Scholar
[6] W. Fulton, Intersection theory. Springer 1984. MR732620 Zbl 0541.1400510.1007/978-3-662-02421-8Search in Google Scholar
[7] J. Kollár, Rational curves on algebraic varieties. Springer 1996. MR1440180 Zbl 0877.1401210.1007/978-3-662-03276-3Search in Google Scholar
[8] J. Kollár, S. Mori, Classification of three-dimensional flips. J. Amer. Math. Soc. 5 (1992), 533–703. MR1149195 Zbl 0773.1400410.1090/S0894-0347-1992-1149195-9Search in Google Scholar
[9] 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
[10] A. A. Roĭtman, Rational equivalence of zero-dimensional cycles (Russian). Mat. Sb. (N.S.) 89(131) (1972), 569–585, 671. English translation: Math. USSR-Sb. 18 (1974), 571–588. MR0327767 Zbl 0259.14003 Zbl 0273.1400110.1070/SM1972v018n04ABEH001860Search in Google Scholar
[11] C. Voisin, Hodge theory and complex algebraic geometry. II. Cambridge Univ. Press 2007. MR2449178 Zbl 1129.14020Search in Google Scholar
© 2017 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
Articles in the same Issue
- Frontmatter
- Classification of 3-dimensional left-invariant almost paracontact metric structures
- On the topology of the spaces of curvature constrained plane curves
- On deformations of parallel G2 structures and almost contact metric structures
- A flag representation of projection functions
- A fundamental theorem for submanifolds of multiproducts of real space forms
- Intriguing sets of quadrics in PG(5, q)
- Successive radii and ball operators in generalized Minkowski spaces
- Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
- The Archimedean projection property
- Kernels of numerical pushforwards
- Modified classical flat Minkowski planes
