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On the Gromov width of homogeneous Kähler manifolds
No full textWe compute the Gromov width of homogeneous Kähler manifolds with second Betti number equal to one. Our result is based on the recent preprint [4] and on the upper bound of the Gromov width for such manifolds obtained in [6]
Some characterizations of the complex projective space via Ehrhart polynomials
Full text linkLet P-lambda Sigma n be the Ehrhart polynomial associated to an integral multiple lambda of the standard simplex Sigma(n) subset of R-n. In this paper, we prove that if (M, L) is an n-dimensional polarized toric manifold with associated Delzant polytope Delta and Ehrhart polynomial P-Delta such that P-Delta = P-lambda Sigma n, for some lambda is an element of Z(+), then (M, L) congruent to (CPn, O(lambda)) (where O (1) is the hyperplane bundle on CPn) in the following three cases: (1) arbitrary n and lambda = 1, (2) n = 2 and lambda = 3 and (3) lambda = n + 1 under the assumption that the polarization L is asymptotically Chow semistable
Canonical metrics on Hartogs domains
Full text linkAn n-dimensional Hartogs domain DF can be equipped with a natural Kähler metric gF. This paper contains two results. In the first one we prove that if gF is an extremal Kähler metric then (DF , gF ) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space. In the second one we prove the same assertion under the assumption that there exists a real holomorphic vector field X on DF such that (gF, X) is a Kähler–Ricci soliton
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