Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE CHOW RING OF A SEQUENCE OF POINT BLOW-UPS

  • Daniel Camazon Portela (Department of Algebra, Analysis, Geometry and Topology University of Valladolid)
  • Received : 2023.06.13
  • Accepted : 2024.05.28
  • Published : 2024.07.31
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Abstract

Given a sequence of point blow-ups of smooth n-dimensional projective varieties Zi defined over an algebraically closed field $k,\,Z_s\,{\overset{{\pi}_s}{\longrightarrow}}\,Z_{s-1}\,{\overset{{\pi}_{s-1}}{\longrightarrow}}\,{\cdots}\,{\overset{{\pi}_2}{\longrightarrow}}\,Z_1\,{\overset{{\pi}_1}{\longrightarrow}}\,Z_0$, with Z0 ≅ ℙn, we give two presentations of the Chow ring A•(Zs) of its sky. The first one uses the classes of the total transforms of the exceptional components as generators and the second one uses the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of the final divisors of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles A0(Zs) of its sky.

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Acknowledgement

I would like to thank the referee for his/her detailed reading of this paper and thoughtful suggestions.

References

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