Semicontinuous maps on module varieties

Abstract

We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper semicontinuous. We also discuss inequalities of generic values of some upper semicontinuous maps.

17 pages. V2: small corrections and slightly reorganized after a referee report. Final version, to appear in Crelle