Cohomological Chow Groups of codimension one of varieties with isolated singularities

TL;DR

This paper computes specific cohomological Chow groups for varieties with isolated singularities, focusing on codimension one groups in higher dimensions under certain topological conditions of the dual complex.

Contribution

It provides new calculations of cohomological Chow groups for varieties with isolated singularities under topological conditions on the dual complex.

Findings

Cohomological Chow groups computed for higher-dimensional varieties with contractible dual complex.

Results for 3-dimensional varieties under the condition $H^{2}( ext{Gamma}(E))=0$.

Examples illustrating the computation of these groups.

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 $H^{2}(\Gamma(E))=0$.