Translator Disclaimer
VOL. 66 | 2015 Smooth double subvarieties on singular varieties. II
Maria del Rosario Gonzalez-Dorrego

Editor(s) Vincent Blanlœil, Osamu Saeki

## 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.

## Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.14012
MathSciNet: MR3382039

Digital Object Identifier: 10.2969/aspm/06610001

Subjects:
Primary: 14B05
Secondary: 14E15, 14J17, 14J30, 14J35, 14J40, 14J70, 32S25