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Higher connectivity of tropicalizations
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AbstractWe show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0 is $$(d-\ell )$$
(
d
-
ℓ
)
-connected through codimension one, where $$\ell $$
ℓ
is the dimension of the lineality space of the tropicalization. From this we obtain a higher connectivity result for skeleta of rational polytopes. We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.
Title: Higher connectivity of tropicalizations
Description:
AbstractWe show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0 is $$(d-\ell )$$
(
d
-
ℓ
)
-connected through codimension one, where $$\ell $$
ℓ
is the dimension of the lineality space of the tropicalization.
From this we obtain a higher connectivity result for skeleta of rational polytopes.
We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.
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