The signed Euler characteristic of very affine varieties

Abstract

A conjecture of J. Huh and B. Sturmfels predicts that the sign of the Euler characteristic of a complex very affine variety depends only on the parity of the dimension. The conjecture is true for locally complete intersections. Beyond this case, we construct counterexamples with arbitrarily bad failure.

v2: More details in the lci case. Final version, to appear in IMRN

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