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The essential skeleton of a product of degenerations
We study the problem of how the dual complex of the special fiber of a strict normal crossings degeneration $\mathscr{X}_{R}$ changes under products. We view the dual complex as a skeleton inside theExpand
Higher Fano Manifolds
In this paper we address Fano manifolds with positive higher Chern characters. They are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, theyExpand
Toric geometry and integral affine structures in non-archimedean mirror symmetry
We study integral dlt models of a proper C((t))-variety X along a toric stratum of the special fiber. We prove that the associated Berkovich retraction from the non-archimedean analytification of XExpand
Essential skeletons of pairs and the geometric P=W conjecture.
We construct weight functions on the Berkovich analytification of a variety over a trivially-valued field of characteristic zero, and this leads to the definition of the Kontsevich-SoibelmanExpand
On the geometric P=W conjecture
We formulate the geometric P=W conjecture for singular character varieties. We establish it for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus. To this end, weExpand