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Mathematics > Algebraic Geometry

arXiv:1805.00183 (math)
[Submitted on 1 May 2018 (v1), last revised 11 Feb 2019 (this version, v2)]

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

Authors: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.
Comments: 50 pages
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14N35, 18E30
Cite as: arXiv:1805.00183 [math.AG]
  (or arXiv:1805.00183v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.00183

Submission history

From: Yukinobu Toda [view email]
[v1] Tue, 1 May 2018 04:32:15 UTC (41 KB)
[v2] Mon, 11 Feb 2019 23:12:15 UTC (41 KB)
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