TY - JOUR
T1 - Convexity of complements of tropical varieties, and approximations of currents
AU - Adiprasito, Karim
AU - Babaee, Farhad
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/2/8
Y1 - 2019/2/8
N2 - The goal of this note is to affirm a local version of conjecture of Nisse–Sottile [19] on higher convexity of complements of tropical varieties, while providing a family of counter-examples for the global Nisse–Sottle conjecture in any codimension and dimension higher than one. Moreover, it is shown that, surprisingly, this family also provides a family of counter-examples for the generalized Hodge conjecture for positive currents in these dimensions, and gives rise to further approximability obstruction.
AB - The goal of this note is to affirm a local version of conjecture of Nisse–Sottile [19] on higher convexity of complements of tropical varieties, while providing a family of counter-examples for the global Nisse–Sottle conjecture in any codimension and dimension higher than one. Moreover, it is shown that, surprisingly, this family also provides a family of counter-examples for the generalized Hodge conjecture for positive currents in these dimensions, and gives rise to further approximability obstruction.
UR - http://www.scopus.com/inward/record.url?scp=85049939476&partnerID=8YFLogxK
U2 - 10.1007/s00208-018-1728-2
DO - 10.1007/s00208-018-1728-2
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AN - SCOPUS:85049939476
SN - 0025-5831
VL - 373
SP - 237
EP - 251
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -