The unreasonable effectiveness of wall-crossing in algebraic geometry
Arend Bayer, Emanuele Macr\`i
TL;DR
This paper surveys how wall-crossing phenomena via Bridgeland stability conditions have significantly advanced algebraic geometry, highlighting key applications and open questions for future exploration.
Contribution
It provides a comprehensive overview of the applications of wall-crossing and Bridgeland stability conditions in algebraic geometry, emphasizing their impact and future directions.
Findings
Wall-crossing techniques have led to breakthroughs in algebraic geometry.
Bridgeland stability conditions connect various geometric invariants.
Open questions suggest rich future research avenues.
Abstract
We survey applications of Bridgeland stability conditions in algebraic geometry and discuss open questions for future research.
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Taxonomy
TopicsNumerical methods for differential equations · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation