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Hypercritical deformed Hermitian-Yang–Mills equation revisited

  • Jianchun Chu EMAIL logo und Man-Chun Lee
Veröffentlicht/Copyright: 17. Mai 2023

Abstract

In this paper, we study the hypercritical deformed Hermitian-Yang–Mills equation on compact Kähler manifolds and resolve two conjectures of Collins–Yau [Moment maps, nonlinear PDE, and stability in mirror symmetry, preprint (2018), https://arxiv.org/abs/1811.04824].

Funding statement: J. Chu was partially supported by the Fundamental Research Funds for the Central Universities, Peking University. M.-C. Lee was supported by the direct grant for research 2021/2022.

References

[1] G. Chen, The J-equation and the supercritical deformed Hermitian–Yang–Mills equation, Invent. Math. 225 (2021), no. 2, 529–602. 10.1007/s00222-021-01035-3Suche in Google Scholar

[2] J. Chu, M.-C. Lee and R. Takahashi, A Nakai–Moishezon type criterion for supercritical deformed Hermitian-Yang–Mills equation, preprint (2021), https://arxiv.org/abs/2105.10725; to appear in J. Differential Geom. Suche in Google Scholar

[3] T. C. Collins, A. Jacob and S.-T. Yau, ( 1 , 1 ) forms with specified Lagrangian phase: A priori estimates and algebraic obstructions, Camb. J. Math. 8 (2020), no. 2, 407–452. 10.4310/CJM.2020.v8.n2.a4Suche in Google Scholar

[4] T. C. Collins and Y. Shi, Stability and the deformed Hermitian–Yang–Mills equation, Surveys in differential geometry 2019. Differential geometry, Calabi–Yau theory, and general relativity. Part 2, Surv. Differ. Geom. 24, International Press, Boston (2022), 1–38. 10.4310/SDG.2019.v24.n1.a1Suche in Google Scholar

[5] T. C. Collins, D. Xie and S.-T. Yau, The deformed Hermitian–Yang–Mills equation in geometry and physics, Geometry and physics. Vol. I, Oxford University, Oxford (2018), 69–90. 10.1093/oso/9780198802013.003.0004Suche in Google Scholar

[6] T. C. Collins and S.-T. Yau, Moment maps, nonlinear PDE, and stability in mirror symmetry, preprint (2018), https://arxiv.org/abs/1811.04824. Suche in Google Scholar

[7] V. Datar and V. P. Pingali, A numerical criterion for generalised Monge–Ampère equations on projective manifolds, Geom. Funct. Anal. 31 (2021), no. 4, 767–814. 10.1007/s00039-021-00577-1Suche in Google Scholar

[8] J.-P. Demailly and M. Păun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2) 159 (2004), no. 3, 1247–1274. 10.4007/annals.2004.159.1247Suche in Google Scholar

[9] A. Jacob and N. Sheu, The deformed Hermitian-Yang–Mills equation on the blowup of P n , preprint (2020), https://arxiv.org/abs/2009.00651. Suche in Google Scholar

[10] N. C. Leung, S.-T. Yau and E. Zaslow, From special Lagrangian to Hermitian–Yang–Mills via Fourier–Mukai transform, Winter school on mirror symmetry, vector bundles and lagrangian submanifolds (Cambridge 1999), AMS/IP Stud. Adv. Math. 23, American Mathematical Society, Providence (2001), 209–225. Suche in Google Scholar

[11] M. Mariño, R. Minasian, G. Moore and A. Strominger, Nonlinear instantons from supersymmetric 𝑝-branes, J. High Energy Phys. (2000), no. 1, Paper 5. 10.1088/1126-6708/2000/01/005Suche in Google Scholar

[12] J. P. Solomon, The Calabi homomorphism, Lagrangian paths and special Lagrangians, Math. Ann. 357 (2013), no. 4, 1389–1424. 10.1007/s00208-013-0946-xSuche in Google Scholar

[13] J. Song, Nakai–Moishezon criterions for complex Hessian equations, preprint (2020), https://arxiv.org/abs/2012.07956. Suche in Google Scholar

[14] A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is 𝑇-duality, Nuclear Phys. B 479 (1996), no. 1–2, 243–259. 10.1016/0550-3213(96)00434-8Suche in Google Scholar

[15] R. P. Thomas, Moment maps, monodromy and mirror manifolds, Symplectic geometry and mirror symmetry (Seoul 2000), World Scientific, River Edge (2001), 467–498. 10.1142/9789812799821_0013Suche in Google Scholar

Received: 2022-06-12
Revised: 2023-04-25
Published Online: 2023-05-17
Published in Print: 2023-08-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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