Results 1 to 10 of about 181 (31)
Pluricomplex Green's functions and Fano manifolds [PDF]
Épijournal de Géométrie Algébrique, 2019 We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
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Uniform K-stability of polarized spherical varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties.
Thibaut Delcroix
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K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
Forum of Mathematics, Sigma, 2023 We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$ . Combining this with the result of Stibitz and Zhuang [SZ19] on a relation between birational superrigidity
In-Kyun Kim, Takuzo Okada, Joonyeong Won
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Smooth approximation of twisted Kähler-Einstein metrics
Advanced Nonlinear Studies, 2023 In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.
Jin Lize, Wang Feng
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The existence of the Kähler–Ricci soliton degeneration
Forum of Mathematics, Pi, 2023 We prove an algebraic version of the Hamilton–Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler–Ricci soliton ...
Harold Blum +3 more
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A polar dual to the momentum of toric Fano manifolds
Complex Manifolds, 2021 We introduce an invariant on the Fano polytope of a toric Fano manifold as a polar dual counterpart to the momentum of its polar dual polytope. Moreover, we prove that if the momentum of the polar dual polytope is equal to zero, then the dual invariant ...
Sano Yuji
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K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, 2022 We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces ...
Hamid Abban, Ziquan Zhuang
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F‐Manifolds and geometry of information
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020 Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
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The Ricci iteration and its applications [PDF]
, 2007 In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics as discretizations of certain geometric flows.
Rubinstein, Yanir A.
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On the lower bound of the K energy and F functional [PDF]
, 2008 Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.Comment: Final version, to appear in Osaka Journal of ...
Li, Haozhao
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