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Cohomological Chow Groups of codimension one of varieties with isolated singularities

Diosel López-Cruz

Abstract

We compute some particular examples of cohomological Chow groups for varieties with isolated singularities. For higher-dimensional varieties, we compute the cohomological Chow groups of codimension one, provided that the dual complex associated to the normal crossing divisor is contractible. For 3-dimensional varieties, we consider a weaker condition on the dual complex, namely $H^{2}(Γ(E))=0$.

Cohomological Chow Groups of codimension one of varieties with isolated singularities

Abstract

We compute some particular examples of cohomological Chow groups for varieties with isolated singularities. For higher-dimensional varieties, we compute the cohomological Chow groups of codimension one, provided that the dual complex associated to the normal crossing divisor is contractible. For 3-dimensional varieties, we consider a weaker condition on the dual complex, namely .
Paper Structure (8 sections, 12 theorems, 42 equations)

This paper contains 8 sections, 12 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Construction of semi-simplicial hyperresolutions
  4. Hanamura's cohomological Chow groups
  5. Computations: codimension one
  6. Motivic cohomology of threefolds
  7. Varieties of higher dimension
  8. Acknowledgements

Key Result

Theorem 1.1

(=Theorem te) Let $X$ be an irreducible projective variety of dimension 3 over $\mathbb{C}$ with isolated singularities, and with dual complex associated to the normal crossing divisor $E$ such that $H^{2}(\Gamma)=0$. Then ${\rm CHC}^{1}(X, m)=0$ for $m \neq -2,-1, 0, 1$, ${\rm CHC}^{1}(X, 1)=\mathb

Theorems & Definitions (26)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Definition 2.1
  • Proposition 2.2
  • proof
  • Remark 2.3
  • Definition 2.4
  • Remark 2.5
  • Proposition 3.1
  • ...and 16 more