Sch\"on complete intersections

Abstract

A complete intersection $f_1=\cdots=f_k=0$ is sch\"on, if $f_1=\cdots=f_j=0$ defines a sch\"on subvariety of an algebraic torus for every $j\leqslant k$. This class includes nondegenerate complete intersections, critical loci of their coordinate projections, other simplest Thom--Boardman and multiple point strata of such projections, generalized Calabi--Yau complete intersections, equaltions of polynomial optimization, hyperplane arrangement complements, and many other interesting special varieties. We study their Euler characteristics, connectednes, Calabi--Yau-ness, tropicalizations, etc., extending (in part conjecturally) the respective classical results about nondegenerate complete intersections.