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In the context of derived algebraic geometry can someone elucidate the intricacies of Bridgeland stability conditions on derived categories of coherent sheaves? Where can one find examples involving moduli spaces of objects in the derived category and their stability walls and how these conditions impact the geometry of algebraic varieties?

Sorry to all if this is a bad question.

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  • $\begingroup$ (As a complete outsider to the topic, this, and especially the second question, sounds like a home work exercise... In that case, instead consider asking at Mathematics.SE explaining what you've tried.) $\endgroup$
    – Jules Lamers
    Commented Nov 26, 2023 at 18:04
  • $\begingroup$ I finished my master's degree in 2018 :) $\endgroup$
    – anon
    Commented Nov 26, 2023 at 18:07
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    $\begingroup$ Very good, and apologies. Then the phrasing just sounds odd to me. $\endgroup$
    – Jules Lamers
    Commented Nov 26, 2023 at 18:08
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    $\begingroup$ This doesn't look like a duplicate at all. Perhaps the OP can clarify: are you specifically interested in variants of the notion in the setting of stable $\infty$-categories? To me it looks more like you're asking for basic examples (in the classical language of derived categories rather than stable $\infty$-categories). $\endgroup$
    – R. van Dobben de Bruyn
    Commented Nov 27, 2023 at 0:56
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    $\begingroup$ That said, I do agree that it is unclear what you're actually asking. Could you maybe include a little background (e.g. a few sentences on what you know already, why you are interested in this, and in what language you are studying this)? $\endgroup$
    – R. van Dobben de Bruyn
    Commented Nov 27, 2023 at 1:00

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Your question was already asked and answered. Below is what I wrote to answer the linked question.

This is chapter 7 of Fosco Loregian's thesis, linked from his webpage. The paper Simone Virili linked to is one of 3 papers making up the thesis. Specifically, Section 7.2.1 discusses the topology, after Bridgeland, and proves the comparison you asked for. The setting is a slight generalization of that of Bridgeland's original papers, as Loregian makes clear.

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    $\begingroup$ It seems better to mark this thread as a duplicate instead of duplicating the answer. Here, say, the sentence "The paper Simone Virili linked to..." seems incomprehensible without looking at that old post. $\endgroup$
    – Z. M
    Commented Nov 26, 2023 at 20:15