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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2023
- DOI:
- 10.48550/arXiv.2302.02085
- arXiv:
- arXiv:2302.02085
- Bibcode:
- 2023arXiv230202085G
- Keywords:
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- Mathematics - Representation Theory;
- 14M99;
- 16E30;
- 16G70
- E-Print:
- 17 pages. V2: small corrections and slightly reorganized after a referee report. Final version, to appear in Crelle