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Solutions to the Hull-Strominger system with torus symmetry

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arxiv 1901.10322 v3 pith:6Q425R6Y submitted 2019-01-29 math.DG hep-thmath.AG

Anna Fino , Gueo Grantcharov , Luigi Vezzoni This is my paper · ORCID
classification math.DGhep-thmath.AG
keywords timeshull-stromingersharpsystemtorusbundlessmoothsolution
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abstract

We construct new smooth solutions to the Hull-Strominger system, showing that the Fu-Yau solution on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. In particular, we prove that, for $13 \leq k \leq 22$ and $14\leq r\leq 22$, the smooth manifolds $S^1\times \sharp_k(S^2\times S^3)$ and $\sharp_r (S^2 \times S^4) \sharp_{r+1} (S^3 \times S^3)$, have a complex structure with trivial canonical bundle and admit a solution to the Hull-Strominger system.

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  1. The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold

    math.DG 2019-09 accept novelty 8.0 of 10

    The Dirichlet problem for complex k-Hessian equations on compact Hermitian manifolds with boundary is solved under the assumption that a smooth subsolution exists.

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