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of 23
pro vyhledávání: '"Lahdili, Abdellah"'
Autor:
Hallam, Michael, Lahdili, Abdellah
We introduce a new weighted version of the Hermite--Einstein equation, along with notions of weighted slope (semi/poly)stability, and prove that a vector bundle admits a weighted Hermite--Einstein metric if and only if it is weighted slope polystable
Externí odkaz:
http://arxiv.org/abs/2408.06267
Let $X$ be a compact K\"ahler manifold. In this paper we study the existence of constant weighted scalar curvature K\"ahler (weighted cscK) metrics on $X$. More precisely, we establish a priori $C^{k}$-estimates ($k\geq 0$) for the K\"ahler potential
Externí odkaz:
http://arxiv.org/abs/2407.09929
Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal K\"ahler metric whose scalar curvature is stri
Externí odkaz:
http://arxiv.org/abs/2407.01871
Given a Kaehler manifold polarised by a holomorphic ample line bundle, we consider the circle bundle associated to the polarisation with the induced transversal holomorphic structure. The space of contact structures compatible with this transversal s
Externí odkaz:
http://arxiv.org/abs/2310.11625
Publikováno v:
Geom. Topol. 27 (2023) 3229-3302
We show that a compact weighted extremal Kahler manifold (as defined by the third named author) has coercive weighted Mabuchi energy with respect to a maximal complex torus in the reduced group of complex automorphisms. This provides a vast extension
Externí odkaz:
http://arxiv.org/abs/2104.09709
Autor:
Lahdili, Abdellah
We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal K\"ahler metrics on a compact K\"ahler manifold introduced in our previous work. This extends a result by Berman--Bernd
Externí odkaz:
http://arxiv.org/abs/2007.01345
Autor:
Lahdili, Abdellah
We introduce a notion of a K\"ahler metric with constant weighted scalar curvature on a compact K\"ahler manifold $X$, depending on a fixed real torus $\mathbb{T}$ in the reduced group of automorphisms of $X$, and two smooth (weight) functions $\math
Externí odkaz:
http://arxiv.org/abs/1808.07811
Autor:
Lahdili, Abdellah
We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge K\"ahler class a conformally K\"ahler, Einstein--Maxwell metric, or more generally, a K\"ahler metric of constant $(\xi, a, p)$-scalar curvature, then this
Externí odkaz:
http://arxiv.org/abs/1710.00235
Autor:
Lahdili, Abdellah
We obtain a structure theorem for the group of holomorphic automorphisms of a conformally K\"ahler, Einstein-Maxwell metric, extending the classical results of Matsushima, Licherowicz and Calabi in the K\"ahler-Einstein, cscK, and extremal K\"ahler c
Externí odkaz:
http://arxiv.org/abs/1708.01507
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