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Quillen metrics and perturbed equations

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We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations—the generalised Monge–Ampère equation, the almost Hitchin system, and the Calabi–Yang–Mills equations. These are all perturbations of already existing equations. Our construction for the generalised Monge–Ampère equation is conditioned on a conjecture from algebraic geometry. In addition, we prove that for small values of the perturbation parameters, some of these equations have solutions.

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Thanks are in order to Harish Seshadri for useful discussions. The author is also grateful to the anonymous referee for useful feedback and to Joel Fine, Rukmini Dey, Leon Takhtajan, Richard Wentworth, Mario Garcia-Fernandez, and Indranil Biswas for answering some questions. The author acknowledges the support of an ECRA Grant from SERB - ECR/2016/001356 and Grant F.510/25/CAS-II/2018(SAP-I) from UGC (Govt. of India). The author was also partially supported by the Infosys Foundation through the Young Investigator Award.

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Correspondence to Vamsi Pritham Pingali.

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Pingali, V.P. Quillen metrics and perturbed equations. Lett Math Phys 110, 1861–1875 (2020).

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Mathematics Subject Classification 2020