The Lefschetz principle in birational geometry: birational twin varieties
Algebraic Geometry
2019-06-17 v2
Abstract
Inspired by the Weak Lefschetz Principle, we study when a smooth projective variety fully determines the birational geometry of some of its subvarieties. In particular, we consider the natural embedding of the space of complete quadrics into the space of complete collineations and we observe that their birational geometry, from the point of view of Mori theory, fully determines each other. When two varieties are related in this way, we call them birational twins. We explore this notion and its various flavors for other embeddings between Mori dream spaces.
Keywords
Cite
@article{arxiv.1811.07714,
title = {The Lefschetz principle in birational geometry: birational twin varieties},
author = {César Lozano Huerta and Alex Massarenti},
journal= {arXiv preprint arXiv:1811.07714},
year = {2019}
}
Comments
15 page. To appear in the volume dedicated to the BGMS Conference 2018 of the Springer Indam Series