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What are the stability conditions in the sense of Kontsevich-Soibelman. I am reading Bridgeland's stability conditions and I've heard people talking about the Kontsevich-Soibelman Stability. I would …

Mixed Hodge Structures, Peters and Steenbrink

Given a smooth affine symplectic variety $V$ with an action of a connected algebraic $G$. If $\mu$ is the moment map, the define the affine quotient to be : $X = \mu^{-1}(0)// G = \text{Spec}\mathbb{ …

This question is motivated by the current interest of Mathematics and Physics community in Wall Crossing. My questions are : What is wall crossing in Physics, what are the reasons for current intere …

This is a question in general sense, but answers about specific examples are also welcome. Why do we need the notion of stability of objects in a category. If we've a subcategory of stable objects, w …

If ${L}$ is a line bundle over a complex manifold, what does the square root line bundle $L^{\frac{1}{2}}$ mean? After some google, I got to know that there are certain conditions for the existence of …

You need the machinery of triangulated categories and homological algebra to understand the mirror symmetry as it stand today, Homological mirror symmetry. But one can get an idea of mirror symmetry w …

I just found an English translation of Serre's FAC at Richard Borcherds' Algebraic Geometry course web page. I really want to read it sometime. I am beginner in Algebraic Geometry, just started learni …

Why do physicists care about the triangulated/derived categories? I mean what are the problems we want to approach using the machinery of triangulated/derived categories. e.g. in homological mirror sy …

I just started reading about Calabi-Yau manifolds and most of the sources I came across defined Calabi-Yau manifold in a different way. I can see that some of them are just same and I can derive one f …

I am interested in learning about the derived categories of coherent sheaves, the work of Bondal/Orlov and T. Bridgeland. Can someone suggest a reference for this, very introductory one with least pre …

First of all, I am sorry for there are a bunch of questions (though all related)and may not be well framed. What are the DT invariants in physics. When one is computing DT invariants for a Calabi-Yau …

I am interested in learning Mirror Symmetry, both from the SYZ and Homological point of view. I am taking a reading course in Mirror Symmetry, which will focus on the SYZ side. I know basic Complex g …