Survey on homological flips and homological flops
Wai-Kit Yeung
TL;DR
This survey reviews recent developments in the study of homological flips and flops, highlighting challenges, failed approaches, and new examples in understanding derived categories under these transformations.
Contribution
It summarizes existing results, discusses limitations of current methods, and introduces new examples related to homological flips and flops.
Findings
Identifies formal problems in relating derived categories under flips and flops.
Documents failed attempts to resolve these issues.
Provides new examples illustrating the concepts.
Abstract
We give a survey for the results in [Yeu20a, Yeu20b, Yeu20c], which attempts to relate the derived categories under general classes of flips and flops. We indicate how the approach fails because of what appears to be a formal problem. We give some ideas, and record some failed attempts, to fix this problem. We also present some new examples.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology