Polystable Poisson structures on Kähler–Einstein Fano manifolds admit constant-scalar-curvature symplectic generalized Kähler metrics for small enough Poisson tensors, settling the semiclassical YTD conjecture on P².
Generalized complex geometry
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field. We provide new examples, including some on manifolds admitting no known complex or symplectic structure. We prove a generalized Darboux theorem which yields a local normal form for the geometry. We show that there is an elliptic deformation theory and establish the existence of a Kuranishi moduli space. We then define the concept of a generalized Kahler manifold. We prove that generalized Kahler geometry is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists. We then use this result to solve an outstanding problem in 4-dimensional bi-Hermitian geometry: we prove that there exists a Riemannian metric on the complex projective plane which admits exactly two distinct Hermitian complex structures with equal orientation. Finally, we introduce the concept of generalized complex submanifold, and show that such sub-objects correspond to D-branes in the topological A- and B-models of string theory.
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Gauge-dressed complex geometry yields heterotic Buscher-like T-duality rules and an extended Born geometry satisfying hypercomplex algebras.
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
The generalized tangent bundle of a parallelizable manifold is trivial, but the converse does not hold, as shown by the Möbius strip, spheres, and projective spaces; it is also related to generalized geometric structures.
Quandles arise from gauge transformation groups on principal bundles, matching generalized Alexander quandles for groups viewed as bundles over a point and extending to Lie and Noether structures in the smooth case.
citing papers explorer
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Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Polystable Poisson structures on Kähler–Einstein Fano manifolds admit constant-scalar-curvature symplectic generalized Kähler metrics for small enough Poisson tensors, settling the semiclassical YTD conjecture on P².
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Gauge-Dressed Complex Geometry and T-duality in Heterotic String Theories
Gauge-dressed complex geometry yields heterotic Buscher-like T-duality rules and an extended Born geometry satisfying hypercomplex algebras.
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On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
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On the triviality of the generalized tangent bundle
The generalized tangent bundle of a parallelizable manifold is trivial, but the converse does not hold, as shown by the Möbius strip, spheres, and projective spaces; it is also related to generalized geometric structures.
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Quandles from gauge transformations
Quandles arise from gauge transformation groups on principal bundles, matching generalized Alexander quandles for groups viewed as bundles over a point and extending to Lie and Noether structures in the smooth case.
- New geometric structures on 3-manifolds: surgery and generalized geometry