%0 Generic %1 huerta2018lefschetz %A Huerta, César Lozano %A Massarenti, Alex %D 2018 %K Birational geometry %T The Lefschetz principle in birational geometry: birational twin varieties %U http://arxiv.org/abs/1811.07714 %X 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.

@misc{huerta2018lefschetz, 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.}, added-at = {2018-11-20T15:27:37.000+0100}, author = {Huerta, César Lozano and Massarenti, Alex}, biburl = {https://www.bibsonomy.org/bibtex/222cba0ab068c4de32d85b7546eddd1ea/taka3617}, description = {The Lefschetz principle in birational geometry: birational twin varieties}, interhash = {4632dd1cf0b46013a4dcd174bcb24dc3}, intrahash = {22cba0ab068c4de32d85b7546eddd1ea}, keywords = {Birational geometry}, note = {cite arxiv:1811.07714Comment: 17 pages. arXiv admin note: text overlap with arXiv:1803.09161, arXiv:1805.10925}, timestamp = {2018-11-20T15:27:37.000+0100}, title = {The Lefschetz principle in birational geometry: birational twin varieties}, url = {http://arxiv.org/abs/1811.07714}, year = 2018 }