논문KCI 등재
ON VOISIN'S CONJECTURE FOR ZERO-CYCLES ON HYPERKAHLER VARIETIES
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Motivated by the Bloch--Beilinson conjectures, Voisin has made a conjecture concerning zero--cycles on self--products of Calabi--Yau varieties. We reformulate Voisin's conjecture in the setting of hyperk\"ahler varieties, and we prove this reformulated conjecture for one family of hyperk\"ahler fourfolds.
Abstract
Motivated by the Bloch--Beilinson conjectures, Voisin has made a conjecture concerning zero--cycles on self--products of Calabi--Yau varieties. We reformulate Voisin's conjecture in the setting of hyperk\"ahler varieties, and we prove this reformulated conjecture for one family of hyperk\"ahler fourfolds.
참고문헌 (33)
- Y. Andre, "Motifs de dimension finie", Seminaire Bourbaki 2003, 2003, pp.299(929) (2004), 115~145
- A. Beauville, "Classification of algebraic and analytic manifolds (Katata, 1982)", pp.1~26 (1983), Birkhauser Boston
- A. Beauville, "Varietes Kahleriennes dont la premiere classe de Chern est nulle", J. Differential Geom, 18(4), pp.755~782 (1983)
- A. Beauville, "Sur l'anneau de Chow d'une variete abelienne", Math. Ann, 273(4), pp.647~651 (1986)
- A. Beauville, "Algebraic cycles and motives" (2007), Cambridge University Press
- A. Beauville, "Some surfaces with maximal Picard number", J. Ec. Polytech. Math, 1, pp.101~116 (2014)
- S. Bloch, "Lectures on Algebraic Cycles" (2010), Cambridge University Press
- S. Bloch, "Remarks on correspondences and algebraic cycles", Amer. J. Math, 105(5), pp.1235~1253 (1983)
- L. Fu, "Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds", Glasg. Math. J, 58(1), pp.17~37 (2016)
- L. Fu, "Motivic hyperkahler resolution conjecture for generalized Kummer varieties", arXiv:1608.04968, ~
- F. Ivorra, "Autour des motifs, Asian-French summer school on algebraic geometry and number theory, Volume III, Panoramas et syntheses" (2011), Societe mathematique de France
- U. Jannsen, "Motivic sheaves and filtrations on Chow groups, In Motives", Proc. Sympos. Pure Math, 55(Part 1), pp.245~302 (1994), Amer. Math. Soc
- U. Jannsen, "Algebraic cycles and motives" (2007), Cambridge University Press
- B. Kahn, "Algebraic cycles and motives" (2007), Cambridge University Press
- T. Katsura, "On Fermat varieties", Tohoku Math. J, 31(1), pp.97~115 (1979)
- K. Kawatani, "On the birational geometry for irreducible symplectic 4-folds related to the Fano schemes of lines", arXiv:0906.0654, ~
- S. Kimura, "Chow groups are finite dimensional, in some sense", Math. Ann, 331(1), pp.173~201 (2005)
- R. Laterveer, "Some results on a conjecture of Voisin for surfaces of geometric genus one", Boll. Unione Mat. Ital, 9(4), pp.435~452 (2016)
- R. Laterveer, "Some desultory remarks concerning algebraic cycles and Calabi-Yau threefolds", Rend. Circ. Mat. Palermo, 65(2), pp.333~344 (2016)
- R. Laterveer, "A remark on the motive of the Fano variety of lines on a cubic", Ann. Math. Que, 41(1), pp.141~154 (2017)
- R. Laterveer, "Algebraic cycles and Todorov surfaces", Kyoto J. Math
- J. Murre, "On a conjectural filtration on the Chow groups of an algebraic variety, parts I and II", Indag. Math, 4(2), pp.177~201 (1993)
- J. Murre, "Lectures on the theory of pure motives" (2013), Amer. Math. Soc
- Y. Namikawa, "Deformation theory of singular symplectic n-folds", Math. Ann, 319(3), pp.597~623 (2001)
- U. Rieβ, "On the Chow ring of birational irreducible symplectic varieties", Manuscripta Math, 145(3-4), pp.473~501 (2014)
- T. Scholl, "Classical motives, In Motives", Proc. Sympos. Pure Math, 55(Part 1), pp.163~187 (1994), Amer. Math. Soc
- M. Shen, "The Fourier transform for certain hyperKahler fourfolds", Mem. Amer. Math. Soc, 240(1139) (2016)
- "Forum Math. Sigma", 2016, 55~
- T. Shioda, "The Hodge conjecture for Fermat varieties", Math. Ann, 245(2), pp.175~184 (1979)
- C. Vial, "On the motive of some hyperkahler varieties", J. Reine Angew. Math, 725, pp.235~247 (2017)
- C. Voisin, "Remarks on zero-cycles of self-products of varieties, In Moduli of vector bundles", Proceedings of the Taniguchi Congress (1994), Marcel Dekker
- C. Voisin, "Chow Rings, Decomposition of the Diagonal, and the Topology of Families" (2014), Princeton University Press
- C. Voisin, "Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kahler varieties, In K3 Surfaces and Their Moduli", Proceedings of the Schiermonnikoog conference 2014 (2016), Birkhauser
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