24 citations · 69 across the 15 of their papers we have counts for
16 papers
Toric geometry of generalized Kähler-Ricci solitons
Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets +1
We establish a local equivalence between toric steady Kähler-Ricci solitons and -type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show thi…
Formal structure of scalar curvature in generalized Kähler geometry
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant alg…
The Riemannian and symplectic geometry of the space of generalized Kähler structures
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
On a compact complex manifold endowed with a holomorphic Poisson tensor and a deRham class , we study the space of generalized Kähler (GK) st…
The generalized Kähler Calabi-Yau problem
Vestislav Apostolov, Xin Fu, Jeffrey Streets +1
We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, wh…
On geometry of steady toric Kähler-Ricci solitons
Yury Ustinovskiy
In this paper we study the gradient steady Kähler-Ricci soliton metrics on non-compact toric manifolds. We show that the orbit space of the free locus of such a manifold carries a…
Variational structure and uniqueness of generalized Kähler-Ricci solitons
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system. We realize solutions as critical points of a functional analogous to the classic…
Generalized Kähler-Ricci flow on toric Fano varieties
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
We study the generalized Kähler-Ricci flow with initial data of symplectic type, and show that this condition is preserved. In the case of a Fano background with toric symmetry, we…
The Gibbons-Hawking ansatz in generalized Kähler geometry
Jeffrey Streets, Yury Ustinovskiy
We derive a local ansatz for generalized Kähler surfaces with nondegenerate Poisson structure and a biholomorphic action which generalizes the classic Gibbons-Hawking ansatz…
Classification of generalized Kähler-Ricci solitons on complex surfaces
Jeffrey Streets, Yury Ustinovskiy
Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that…
On the Structure of Hermitian Manifolds with Semipositive Griffiths Curvature
Yury Ustinovskiy
In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary sm…
Lie-Algebraic Curvature Conditions preserved by the Hermitian Curvature Flow
Yury Ustinovskiy
The purpose of this paper is to prove that the Hermitian Curvature Flow (HCF) on an Hermitian manifold preserves many natural curvature positivity conditions. Following W…
Hermitian curvature flow on complex homogeneous manifolds
Yury Ustinovskiy
In this paper we study a version of the Hermitian curvature flow (HCF). We focus on complex homogeneous manifolds equipped with induced metrics. We prove that this finite-dimension…
On face numbers of flag simplicial complexes
Yury Ustinovskiy
Denham, Suciu and Panov, Ray computed ranks of homotopy groups and Poincaré series of a moment-angle-complex ) / Davis-Januzskiewicz space a…
The Hermitian curvature flow on manifolds with non-negative Griffiths curvature
Yury Ustinovskiy
In this paper we study a particular version of the Hermitian curvature flow (HCF) over a compact complex Hermitian manifold . We prove that if the initial metric has Griff…
Projective toric generators in the unitary cobordism ring
Yury Ustinovskiy, Grigory Solomadin
By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $Ω^U_*\simeq \mathbb Z[a_1,a_2,\…
Complex geometry of moment-angle manifolds
Taras Panov, Yuri Ustinovsky, Misha Verbitsky
Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, c…