I want to riff a bit on Vivek’s “microlocal test curves” and in particular try to synthesize it with David’s calculation from earlier in the summer that the trivialization of a cone over a disk looks like a cluster variable. TLDR: monodromy trivialization homotopies are exactly the data of “wrong-way parallel transport” across a negative …
Wrote this a week or two ago but didn’t post, it’s mostly to try to get my own head straight about previous correspondences on the issues of asking whether the functor of MR1 sheaves is “really” a derived stack, and asking whether it is represented by an algebraic stack. The main point is A) these …
Summary of discussion with David the other night – let me know if anything sounds wrong: Claim: Let $\Sigma \subset N_\mathbb{R} \cong \mathbb{R}^2$ be a complete fan, $\Lambda_\Sigma \subset T^* (M_\mathbb{R}/M)$ the associated Lagrangian, and $n \in N_\mathbb{R}$. Let $\mu_n: Sh_{cc}(M_\mathbb{R}/M, \Lambda_\Sigma) \to dg-Vect$ take a sheaf to its microstalk at $(M,n)$. If $-n$ is …
A quasi-summary (to be taken with a grain of salt) of my understanding of the paper Eric alluded to as well as the paper of Smith on the $A_1$ Hitchin 3-folds, mostly to draw out some subtle differences between the two settings that might reward reflection. 3-folds from Toric Spectral Curves Start with a complete …
This is an amplification of the previous post to the case where $C$ is a curve in an arbitrary linear system $\Delta$ on an arbitrary toric surface $X_\Sigma$. In other words, its purpose is to explain why the result of that computation was “obvious.” Write $\Lambda_1$ for the subset of $\Lambda_\Sigma$ corresponding to the 1-dimensional …
It’s definitely not a good thing to have to go to this website to see if anything new has happened — for example, I just missed several weeks of content because I thought nothing was happening! Wordpress is definitely up to the task of sending email alerts to users when there are new posts/comments (indeed, …
Let me recall what an ideal web is, then throw out a partially-baked question regarding their relationship to exact Lagrangians. The notion of ideal web appears in unpublished work of Goncharov (see here: http://people.math.umass.edu/~tevelev/AGNES_vids/Goncharov.mp4), but builds on a lot of pictures familiar from earlier work of e.g. Postnikov and relates those pictures to his work …