LetX ↪→ P be a smooth, linearly normal algebraic curve. We show that the asymptotics of the Mabuchi energy are completely determined by the discriminant polytope and the Chow polytope of X . From this we deduce a new and entirely algebraic proof that the Mabuchi energy of the rational normal curve of degree d ≥ 2 is bounded below along all degenerations. We conclude that the Moser-Trudinger-Ono...

We aimed to explore the cerebellar cortical inputs from two spinocerebellar pathways, the spinal border cell-component of the ventral spinocerebellar tract (SBC-VSCT) and the dorsal spinocerebellar tract (DSCT), respectively, in the sublobule C1 of the cerebellar posterior lobe. The two pathways were activated by electrical stimulation of the contralateral lateral funiculus (coLF) and the ipsil...

The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson Miller (2005) via antidiagonal Gr\"obner degeneration matrix varieties. We consider instead diagonal degenerations. In this dual setting, Knutson, Miller, Yong (2009) obtained alternative combinatorics for the class "vexillary'' initiate a study general degenerations, r...

We find restrictions on the topology of tropical varieties that arise from a certain natural class of varieties. We develop a theory of tropical degenerations that is a nonconstant coefficient analogue of Tevelev’s theory of tropical compactifications, and use it to construct normal crossings degenerations of a subvariety X of a torus, under mild hypotheses on X. These degenerations allow us to...

The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a linear space V under linear transformations of V ; or equivalently, it describes the closure of an orbit of GL(V ) acting diagonally on the product of two flag varieties. We consider the degenerations of a triple consisting of two flags and a line, or equivalently the closure of an orbit of GL(V ) ...

Purpose: To disclose the association between spinocerebellar ataxia with oculomotor apraxia and high grade (7 diopters) congenital astigmatism. Methods: Single observational case report. A 39-year-old patient affected by spinocerebellar ataxia from the age of 20 was submitted to genetic and ophthalmic investigations to reach a diagnosis. Results: Genetic testing did not lead to a sure diagnosis...