## Advanced Studies in Pure Mathematics

### Smooth double subvarieties on singular varieties. II

Maria del Rosario Gonzalez-Dorrego

#### Abstract

Let k be an algebraically closed field of characteristic 0. We give a brief survey on multiplicity-2 structures on varieties. Let $Z$ be a reduced irreducible nonsingular $(n-1)$-dimensional variety such that $2Z = X \cap F$, where $X$ is a normal $n$-fold with canonical singularities, $F$ is an $(N-1)$-fold in $\mathbb{P}^N$, such that $Z \cap \mathrm{Sing}(X) \neq \emptyset$. Assume that $\mathrm{Sing}(X)$ is equidimensional and $\mathrm{codim}_X(\mathrm{Sing}(X)) = 3$. We study the singularities of $X$ through which $Z$ passes. We also consider Fano cones. We discuss the construction of some vector bundles and the resolution property of a variety.

#### Article information

Dates
Revised: 14 January 2013
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/ euclid.aspm/1539916276

Digital Object Identifier
doi:10.2969/aspm/06610001

Mathematical Reviews number (MathSciNet)
MR3382039

Zentralblatt MATH identifier
1360.14012

Keywords
$n$-fold singularity intersection

#### Citation

Gonzalez-Dorrego, Maria del Rosario. Smooth double subvarieties on singular varieties. II. Singularities in Geometry and Topology 2011, 1--11, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06610001. https://projecteuclid.org/euclid.aspm/1539916276