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The signed Euler characteristic of very affine varieties. (English) Zbl 1362.14062
Summary: A conjecture of J. Huh and B. Sturmfels [Lect. Notes Math. 2108, 63–117 (2014; Zbl 1328.14004)] 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.

MSC:
14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
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