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2 results

  • SubRiemannian Geometry on the Sphere 𝕊3

  • Ovidiu Calin, Der-Chen Chang, Irina Markina
  • Journal:
    Canadian Journal of Mathematics / Volume 61 / Issue 4 / 01 August 2009
    Published online by Cambridge University Press:
    20 November 2018, pp. 721-739
    Print publication:
    01 August 2009
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  • We discuss the subRiemannian geometry induced by two noncommutative vector fields which are left invariant on the Lie group ${{\mathbb{S}}^{3}}$.

  • NORI’S CONNECTIVITY THEOREM AND HIGHER CHOW GROUPS

  • Claire Voisin
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 1 / Issue 2 / April 2002
    Published online by Cambridge University Press:
    24 January 2003, pp. 307-329
    Print publication:
    April 2002

  • Nori’s connectivity theorem compares the cohomology of $X\times B$ and $Y_B$, where $Y_B$ is any locally complete quasiprojective family of sufficiently ample complete intersections in $X$. When $X$ is the projective space, and we consider hypersurfaces of degree $d$, it is possible to give an explicit bound for $d$, sufficient to conclude that the Connectivity Theorem holds. We show that this bound is optimal, by constructing for lower $d$ classes on $Y_B$ not coming from the ambient space. As a byproduct we get the non-triviality of the higher Chow groups of generic hypersurfaces of degree $2n$ in $\mathbb{P}^{n+1}$.

    AMS 2000 Mathematics subject classification: Primary 14C25; 14D07; 14J70