Higher connectivity of tropicalizations
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.
1984 ◽
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2004 ◽
Vol 321
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pp. 244-251
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1970 ◽
Vol 76
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pp. 767-772
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2018 ◽
Vol 32
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pp. 1850043
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2010 ◽
Vol 82
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pp. 10-17
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2018 ◽
Vol 2020
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pp. 9011-9074
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