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- W3040969306 abstract "In this paper we provide an explicit formula for the optimal lower bound of Donaldson's J-functional, in the sense of finding explicitly the optimal constant in the definition of coercivity, which always exists and takes negative values in general. This constant is positive precisely if the J-equation admits a solution, and the explicit formula has a number of applications. First, this leads to new existence criteria for constant scalar curvature Kahler (cscK) metrics in terms of Tian's alpha invariant. Moreover, we use the above formula to discuss Calabi dream manifolds and an analogous notion for the J-equation, and show that for surfaces the optimal bound is an explicitly computable rational function which typically tends to minus infinity as the underlying class approaches the boundary of the Kahler cone, even when the underlying Kahler classes admit cscK metrics. As a final application we show that if the Lejmi-Sz'ekelyhidi conjecture holds, then the optimal bound coincides with its algebraic counterpart, the set of J-semistable classes equals the closure of the set of uniformly J-stable classes in the Kahler cone, and there exists an optimal degeneration for uniform J-stability." @default.
- W3040969306 created "2020-07-16" @default.
- W3040969306 creator A5078083468 @default.
- W3040969306 date "2020-11-01" @default.
- W3040969306 modified "2023-09-27" @default.
- W3040969306 title "Optimal lower bounds for Donaldson's J-functional" @default.
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- W3040969306 doi "https://doi.org/10.1016/j.aim.2020.107271" @default.
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