Lagrangian skeleta, collars and duality

Fuente: arXiv
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Main Authors: Ballico, Edoardo, Gasparim, Elizabeth, Rubilar, Francisco, Suzuki, Bruno
Format: Preprint
Published: 2021
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author Ballico, Edoardo
Gasparim, Elizabeth
Rubilar, Francisco
Suzuki, Bruno
author_facet Ballico, Edoardo
Gasparim, Elizabeth
Rubilar, Francisco
Suzuki, Bruno
contents We present a geometric realization of the duality between skeleta in $T^*\mathbb P^n$ and collars of local surfaces. Such duality is predicted by combining two auxiliary types of duality: on one side, symplectic duality between $T^*\mathbb P^n$ and a crepant resolution of the $A_n$ singularity; on the other side, toric duality between two types of isolated quotient singularities. We give a correspondence between Lagrangian submanifolds of the cotangent bundle and vector bundles on collars, and describe those birational transformations within the skeleton which are dual to deformations of vector bundles.
format Preprint
id arxiv_https___arxiv_org_abs_2112_09540
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Lagrangian skeleta, collars and duality
Ballico, Edoardo
Gasparim, Elizabeth
Rubilar, Francisco
Suzuki, Bruno
Symplectic Geometry
Algebraic Geometry
53D05, 14D20
We present a geometric realization of the duality between skeleta in $T^*\mathbb P^n$ and collars of local surfaces. Such duality is predicted by combining two auxiliary types of duality: on one side, symplectic duality between $T^*\mathbb P^n$ and a crepant resolution of the $A_n$ singularity; on the other side, toric duality between two types of isolated quotient singularities. We give a correspondence between Lagrangian submanifolds of the cotangent bundle and vector bundles on collars, and describe those birational transformations within the skeleton which are dual to deformations of vector bundles.
title Lagrangian skeleta, collars and duality
topic Symplectic Geometry
Algebraic Geometry
53D05, 14D20
url https://arxiv.org/abs/2112.09540