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A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$

100%

Coppens M.

Open Mathematics

2016

tom 14

nr 1

1-12

For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1$w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

A tropical view on Bruhat-Tits buildings and their compactifications

100%

Werner A.

Open Mathematics

2011

tom 9

nr 2

390-402

We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation and that it is related to the tropicalization of the hypersurface given by the character of the representation.

Ograniczanie wyników

2 Open Mathematics

1 Coppens M.

1 Werner A.

1 2016

1 2011

Wyniki wyszukiwania

A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$

A tropical view on Bruhat-Tits buildings and their compactifications