Algebraic cycles and intersections of a quadric and a cubic

References

[1] A. Beauville, Sur l’anneau de Chow d’une variété abélienne, Math. Ann. 273 (1986), no. 4, 647–651. 10.1007/BF01472135Search in Google Scholar

[2] A. Beauville, On the splitting of the Bloch–Beilinson filtration, Algebraic Cycles and Motives. Vol. 2, London Math. Soc. Lecture Note Ser. 344, Cambridge University, Cambridge (2007), 38–53. 10.1017/CBO9781107325968.004Search in Google Scholar

[3] A. Beauville and C. Voisin, On the Chow ring of a K⁢3 surface, J. Algebraic Geom. 13 (2004), no. 3, 417–426. 10.1090/S1056-3911-04-00341-8Search in Google Scholar

[4] N. Bergeron and Z. Li, Tautological classes on moduli spaces of hyper-Kähler manifolds, Duke Math. J. 168 (2019), no. 7, 1179–1230. 10.1215/00127094-2018-0063Search in Google Scholar

[5] H. Diaz, The Chow ring of a cubic hypersurface, Int. Math. Res. Not. IMRN (2019), 10.1093/imrn/rnz299. 10.1093/imrn/rnz299Search in Google Scholar

[6] D. Favero, A. Iliev and L. Katzarkov, On the Griffiths groups of Fano manifolds of Calabi–Yau Hodge type, Pure Appl. Math. Q. 10 (2014), no. 1, 1–55. 10.4310/PAMQ.2014.v10.n1.a1Search in Google Scholar

[7] L. Fu, R. Laterveer and C. Vial, Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type, Ann. Mat. Pura Appl. (4) (2019), 10.1007/s10231-020-01060-8. 10.1007/s10231-020-01060-8Search in Google Scholar

[8] L. Fu, R. Laterveer and C. Vial, The generalized Franchetta conjecture for some hyper-Kähler varieties, J. Math. Pures Appl. (9) 130 (2019), 1–35. 10.1016/j.matpur.2019.01.018Search in Google Scholar

[9] L. Fu, R. Laterveer and C. Vial, The generalized Franchetta conjecture for some hyper-Kähler varieties. II, preprint (2020), https://arxiv.org/abs/2002.05490. 10.5802/jep.166Search in Google Scholar

[10] L. Fu, Z. Tian and C. Vial, Motivic hyper-Kähler resolution conjecture, I: Generalized Kummer varieties, Geom. Topol. 23 (2019), no. 1, 427–492. 10.2140/gt.2019.23.427Search in Google Scholar

[11] L. Fu and C. Vial, Distinguished cycles on varieties with motive of Abelian type and the section property, J. Algebraic Geom. 29 (2020), no. 1, 53–107. 10.1090/jag/729Search in Google Scholar

[12] W. Fulton, Intersection Theory, Ergeb. Math. Grenzgeb. (3) 2, Springer, Berlin, 1984. 10.1007/978-3-662-02421-8Search in Google Scholar

[13] M. Green and P. Griffiths, An interesting 0-cycle, Duke Math. J. 119 (2003), no. 2, 261–313. 10.1215/S0012-7094-03-11923-7Search in Google Scholar

[14] D. Huybrechts, The geometry of cubic hypersurfaces, Lecture Notes, https://www.math.uni-bonn.de/people/huybrech/. Search in Google Scholar

[15] A. Iliev and L. Manivel, Fano manifolds of Calabi–Yau Hodge type, J. Pure Appl. Algebra 219 (2015), no. 6, 2225–2244. 10.1016/j.jpaa.2014.07.033Search in Google Scholar

[16] U. Jannsen, On finite-dimensional motives and Murre’s conjecture, Algebraic Cycles and Motives. Vol. 2, London Math. Soc. Lecture Note Ser. 344, Cambridge University, Cambridge (2007), 112–142. 10.1017/CBO9781107325968.008Search in Google Scholar

[17] S.-I. Kimura, Chow groups are finite dimensional, in some sense, Math. Ann. 331 (2005), no. 1, 173–201. 10.1007/s00208-004-0577-3Search in Google Scholar

[18] R. Laterveer, A remark on the chow ring of Küchle fourfolds of type d3, Bull. Aust. Math. Soc. 100 (2019), no. 3, 410–418. 10.1017/S0004972719000273Search in Google Scholar

[19] R. Laterveer, Algebraic cycles and Verra fourfolds, Tohoku Math. J. (2) 72 (2020), no. 3, 451–485. 10.2748/tmj/1601085625Search in Google Scholar

[20] R. Laterveer, On the Chow ring of certain Fano fourfolds, Ann. Univ. Paedagog. Crac. Stud. Math. 19 (2020), 39–52. 10.2478/aupcsm-2020-0004Search in Google Scholar

[21] R. Laterveer, On the Chow ring of Fano varieties of type S2, Abh. Math. Semin. Univ. Hambg. 90 (2020), no. 1, 17–28. 10.1007/s12188-020-00218-8Search in Google Scholar

[22] R. Laterveer, Algebraic cycles and Gushel-Mukai fivefolds, J. Pure Appl. Algebra 225 (2021), no. 5, Article ID 106582. 10.1016/j.jpaa.2020.106582Search in Google Scholar

[23] R. Laterveer, Algebraic cycles and Fano threefolds of genus 8, preprint. 10.4171/PM/2069Search in Google Scholar

[24] R. Laterveer and C. Vial, On the Chow ring of Cynk–Hulek Calabi–Yau varieties and Schreieder varieties, Canad. J. Math. 72 (2020), no. 2, 505–536. 10.4153/S0008414X19000191Search in Google Scholar

[25] C. Lehn, Twisted cubics on singular cubic fourfolds—on Starr’s fibration, Math. Z. 290 (2018), no. 1–2, 379–388. 10.1007/s00209-017-2021-xSearch in Google Scholar

[26] J. P. Murre, On a conjectural filtration on the Chow groups of an algebraic variety. I. The general conjectures and some examples, Indag. Math. (N. S.) 4 (1993), no. 2, 177–188. 10.1016/0019-3577(93)90038-ZSearch in Google Scholar

[27] J. P. Murre, J. Nagel and C. A. M. Peters, Lectures on the Theory of Pure Motives, Univ. Lecture Ser. 61, American Mathematical Society, Providence, 2013. 10.1090/ulect/061Search in Google Scholar

[28] N. Pavic, J. Shen and Q. Yin, On O’Grady’s generalized Franchetta conjecture, Int. Math. Res. Not. IMRN 2017 (2017), no. 16, 4971–4983. 10.1093/imrn/rnw158Search in Google Scholar

[29] A. J. Scholl, Classical motives, Motives (Seattle 1991), Proc. Sympos. Pure Math. 55, American Mathematical Society, Providence (1994), 163–187. 10.1090/pspum/055.1/1265529Search in Google Scholar

[30] M. Shen and C. Vial, The Fourier transform for certain hyperkähler fourfolds, Mem. Amer. Math. Soc. 240 (2016), no. 1139, 1–163. 10.1090/memo/1139Search in Google Scholar

[31] M. Shen and C. Vial, The motive of the Hilbert cube X[3], Forum Math. Sigma 4 (2016), Paper No. e30. 10.1017/fms.2016.25Search in Google Scholar

[32] M. Tavakol, The tautological ring of the moduli space M2,nr⁢t, Int. Math. Res. Not. IMRN 2014 (2014), no. 24, 6661–6683. 10.1093/imrn/rnt178Search in Google Scholar

[33] M. Tavakol, Tautological classes on the moduli space of hyperelliptic curves with rational tails, J. Pure Appl. Algebra 222 (2018), no. 8, 2040–2062. 10.1016/j.jpaa.2017.08.019Search in Google Scholar

[34] C. Vial, On the motive of some hyperKähler varieties, J. Reine Angew. Math. 725 (2017), 235–247. 10.1515/crelle-2015-0008Search in Google Scholar

[35] Q. Yin, Finite-dimensionality and cycles on powers of K⁢3 surfaces, Comment. Math. Helv. 90 (2015), no. 2, 503–511. 10.4171/CMH/362Search in Google Scholar

[36] Q. Yin, The generic nontriviality of the Faber-Pandharipande cycle, Int. Math. Res. Not. IMRN 2015 (2015), no. 5, 1263–1277. 10.1093/imrn/rnt252Search in Google Scholar