Curve counting via stable objects in derived categories of Calabi-Yau 4-folds - INSPIRE

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Curve counting via stable objects in derived categories of Calabi-Yau 4-folds

Yalong Cao
(
- Tokyo U., IPMU
)
,
Yukinobu Toda
(
- Tokyo U., IPMU
)

Sep 11, 2019

34 pages

Published in:

Adv.Math. 406 (2022) 108531

Published: Sep 17, 2022

e-Print:

1909.04897 [math.AG]

DOI:

10.1016/j.aim.2022.108531 (publication)

View in:

ADS Abstract Service

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Abstract: (Elsevier Inc.)

In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The purpose of this paper is to give an interpretation of the above GV type formula in terms of wall-crossing phenomena in the derived category. We introduce invariants counting LePotier's stable pairs on CY 4-folds, and show that they count certain stable objects in D0-D2-D8 bound states in the derived category. We propose a conjectural wall-crossing formula for the generating series of our invariants, which recovers the conjectural GV type formula. Examples are computed for both compact and toric cases to support our conjecture.

Note:

34 pages. Published version

14N35
14J32
Gopakumar-Vafa type invariants
Le Potier stable pairs
Wall-crossing
Calabi-Yau 4-folds
category: Calabi-Yau
stability
bound state

References(43)

Figures(0)

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