Families of stable 3-folds in positive characteristic
J\'anos Koll\'ar

TL;DR
This paper demonstrates that in positive characteristic, flat families of stable 3-folds do not produce proper moduli spaces, and it constructs examples of log canonical 4-fold pairs with non-weakly normal centers.
Contribution
It reveals fundamental limitations in moduli space construction for stable 3-folds in positive characteristic and provides explicit examples of non-weakly normal log canonical centers.
Findings
Flat families of stable 3-folds are not proper in characteristic p>0
Constructs log canonical 4-fold pairs with non-weakly normal centers
Highlights challenges in moduli theory in positive characteristic
Abstract
We show that flat families of stable 3-folds do not lead to proper moduli spaces in any characteristic . As a byproduct, we obtain log canonical 4-fold pairs, whose log canonical centers are not weakly normal.
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Taxonomy
TopicsGraph Labeling and Dimension Problems
