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arXiv · 1805.00183

Semiorthogonal decompositions of stable pair moduli spaces via d-critical flips

Yukinobu Toda
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Abstract

We show the existence of semiorthogonal decompositions (SOD) of Pandharipande-Thomas (PT) stable pair moduli spaces on Calabi-Yau 3-folds with irreducible curve classes, assuming relevant moduli spaces are non-singular. The above result is motivated by categorifications of wall-crossing formula of PT invariants in the derived category, and also a d-critical analogue of Bondal-Orlov, Kawamata's D/K equivalence conjecture. We also give SOD of stable pair moduli spaces on K3 surfaces, which categorifies Kawai-Yoshioka's formula proving Katz-Klemm-Vafa formula for PT invariants on K3 surfaces with irreducible curve classes.

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Yukinobu Toda. 2018-05-01. Semiorthogonal decompositions of stable pair moduli spaces via d-critical flips. https://arxiv.org/abs/1805.00183

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