Schön complete intersections

A complete intersection $f_1=\cdots =f_k=0$ is schön, if $f_1=\cdots =f_j=0$ defines a schön subvariety of an algebraic torus for every $j⩽k$. 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.