Global resolution of singularities in $1$-dimensional foliated spaces

André Belotto

Global resolution of singularities in $1$-dimensional foliated spaces

Complex Variables 2016-11-04 v3 Algebraic Geometry

Authors: André Belotto

Abstract

Let $M$ be an analytic manifold over $\mathbb{R}$ or $\mathbb{C}$ , $\theta$ a $1$ -dimensional Log-Canonical (resp. monomial) singular distribution and $\mathcal{I}$ a coherent ideal sheaf defined on $M$ . We prove the existence of a resolution of singularities for $\mathcal{I}$ that preserves the Log-Canonicity (resp. monomiality) of the singularities of $\theta$ . Furthermore, we apply this result to provide a resolution of a family of ideal sheaves when the dimension of the parameter space is equal to the dimension of the ambient space minus one.

Keywords

resolution of singularities foliated spaces analytic manifold log-canonical distribution monomial distribution coherent ideal sheaf global resolution

Cite

@article{arxiv.1211.2308,
  title  = {Global resolution of singularities in $1$-dimensional foliated spaces},
  author = {André Belotto},
  journal= {arXiv preprint arXiv:1211.2308},
  year   = {2016}
}

Comments

There is a change of title and structure to the previous version of the manuscript, although the results are the same. We intend to make the manuscript more direct

Global resolution of singularities in $1$-dimensional foliated spaces

Abstract

Keywords

Cite

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