Hall algebras in the derived category and higher rank DT invariants

Yukinobu Toda

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arXiv · 1601.07519

Hall algebras in the derived category and higher rank DT invariants

Yukinobu Toda

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Abstract

We remark that the combination of the works of Ben-Bassat-Brav-Bussi-Joyce and Alper-Hall-Rydh imply the conjectured local description of the moduli stacks of semi-Schur objects in the derived category of coherent sheaves on projective Calabi-Yau 3-folds. This result was assumed in the author's previous papers to apply wall-crossing formulas of DT type invariants in the derived category, e.g. DT/PT correspondence, rationality, etc. We also show that the above result is applied to prove the higher rank version of DT/PT correspondence and rationality.

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Yukinobu Toda. 2016-01-28. Hall algebras in the derived category and higher rank DT invariants. https://arxiv.org/abs/1601.07519

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