The Chow groups of Hilb 4 P 2 and a base for A 2 ,A 3 ,A 2d−2 ,A 2d−3 of Hilb d P

Mallavibarrena Martínez de Castro, Raquel2023-06-212023-06-211986-10-300764-4442https://hdl.handle.net/20.500.14352/64679G. Ellingsrud and S. A. Strømme [Invent. Math. 87 (1987), no. 2, 343–352; see the following review] have proved that the Chow group of the Hilbert scheme Hilb d P 2 is free and have computed the ranks of its homogeneous parts A i (Hilb d P 2 ) . In the present note, the author introduces a family of cycles in Hilb d P 2 and conjectures this family to be a basis of the Chow group. In the case d=3 , this follows from a paper by G. Elencwajg and P. Le Barz [C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 12, 635–638; MR0814963 (87c:14006)]. Here the conjecture is proved in case d=4 , and for any d , in the cases i=2,3,2d−3, 2d−2 . The proof consists in calculations of intersection matrices.fraThe Chow groups of Hilb 4 P 2 and a base for A 2 ,A 3 ,A 2d−2 ,A 2d−3 of Hilb d Pjournal articlehttp://gallica.bnf.fr/ark:/12148/bpt6k5744587p/f71.image.r=COMPTES%20RENDUS%20DE%20L%20ACADEMIE%20DES%20SCIENCES%20SERIE%20I-MATHEMATIQUE.langESrestricted access512.1Chow groups and ringsGeometria algebraica1201.01 Geometría Algebraica