We compute the Dolbeault cohomology of minimally stable polytopal LVM manifolds using a finite curvature complex. Let $B$ be the indispensable weight block. A canonical exact sequence identifies the kernel of the curvature map with $(\operatorname{coker}B)^\vee$ and its cokernel with $(\ker B)^\vee$. At full rank, the...
L. Katzarkov, Kyoung-Seog Lee, Ernesto Lupercio et al.· 0 citations
In this paper we prove that a process we call tropical relaxation gives a convergent method for numerically approximating the Monge--Amp\`ere Dirichlet problem on bounded convex planar domains. We approximate the prescribed probability measure by point clouds and construct the least concave tropical roof with zero boun...
N. Kalinin, Ernesto Lupercio, Higinio Serrano et al.· 2 citations
Let $\X$ be a Hausdorff second-countable smooth orbifold without boundary, possibly noncompact and ineffective. Suppose $\dim\X\leq n$ and $|G_x|\leq B$ for integers $n\geq0$ and $B\geq1$, where $G_x$ is the full stabilizer at $x$. We construct a smooth Hermitian bundle of explicit rank $R(n,B)$ whose fibre at $x$ is a...
We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of the underlying lattice is much larger than the number of random perturbation points distributed according to a prescribed probability measure...
We prove a quantitative tropical approximation to the planar Aleksandrov Monge--Amp\`ere equation. Let $\Omega\subset\mathbb R^2$ be a bounded open convex domain, fix $K\Subset\Omega$, and let $F_N=G_{P_N}(0_\Omega)$ be the minimal nonnegative concave tropical series with integral slopes, zero boundary values, and corn...
N. Kalinin, Ernesto Lupercio, Higinio Serrano et al.· 2 citations
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