Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Author "Dervan, Ruadhai"
Now showing items 1-7 of 7
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A finite dimensional approach to Donaldson's J-flow
Dervan, Ruadhai; Keller, JConsider a projective manifold with two distinct polarisations $L_1$ and $L_2$. From this data, Donaldson has defined a natural flow on the space of Kähler metrics in $c_1$($L_1$), called the J-flow. The existence of a ...
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Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
Dervan, Ruadhai (Université Paul SabatierAnnales de la Faculté des Sciences de Toulouse, 2016)We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the ...
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Alpha Invariants and K-Stability for General Polarizations of Fano Varieties
Dervan, Ruadhai (Oxford University PressINTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014-09-26)We provide a sufficient condition for polarisations of Fano varieties to be K-stable in terms of Tian’s alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system ...
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K-stability for Kähler manifolds
Dervan, Ruadhai; Ross, Julius Andrew (International PressMathematical Research Letters, 2017-09)We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. ...
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Non-reductive automorphism groups, the Loewy filtration and K-stability
Codogni, Giulio; Dervan, Ruadhai (l'Institut FourierAnnales de l'Institut Fourier, 2016-03-18)We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several ...
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On K-stability of finite covers
Dervan, Ruadhai (Oxford University PressJournal of the London Mathematical Society, 2016)We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler-Einstein metrics, including hypersurfaces, double solids and threefolds.
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Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
Dervan, Ruadhai (Oxford University PressInternational Mathematics Research Notices, 2015-10-14)We introduce a norm on the space of test configurations, called the minimum norm. We conjecture that uniform K-stability is equivalent to the existence of a constant scalar curvature Kähler metric. This uniformity is ...