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1 results

  • Chern Classes of Splayed Intersections

  • Paolo Aluffi, Eleonore Faber
  • Journal:
    Canadian Journal of Mathematics / Volume 67 / Issue 6 / 01 December 2015
    Published online by Cambridge University Press:
    20 November 2018, pp. 1201-1218
    Print publication:
    01 December 2015
    • Article
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  • We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern–Schwartz–MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a strong splayedness assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern–Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.