Variation of GIT and variation of Lagrangian skeletons I: Flip and flop

The coherent-constructible correspondence for toric variety assigns to each $n$ -dimensional toric variety $X_{Σ}$ a Lagrangian skeleton $Λ_{Σ} \subset T^{*} T^{n}$ , such that the derived category of coherent sheaves $Coh (X_{Σ})$ is equivalent to the (wrapped) constructible sheaves $S h^{w} (T^{n}, Λ_{Σ})$ . In this paper, we extend this correspondence, so that flip and flop between toric varieties corresponds to variation of Lagrangian skeletons. The main idea is to translate the window subcategory in variation of GIT to a window skeleton.

PDF Access Denied

We have not been able to recognize your IP address 216.73.216.187 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

variation of GIT, Lagrangian skeleton, toric mirror symmetry

Mathematical Subject Classification

Primary: 53D37

Milestones

Received: 9 May 2022

Revised: 4 June 2024

Accepted: 25 June 2024

Published: 7 March 2025

Authors

Peng Zhou
University of California, Berkeley Berkeley, CA United States

Vol. 7, No. 1, 2025

Peng Zhou

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors