A connectedness theorem over the spectrum of a formal power series ring
Masayuki Kawakita
TL;DR
This paper investigates the connectedness properties of certain loci in formal power series rings, establishing key results in dimension 3 related to minimal log discrepancies and lc centers.
Contribution
It proves the existence and normality of the smallest lc center in dimension 3 and applies this to the ACC for minimal log discrepancies above 1.
Findings
Proves connectedness of non-subklt locus over formal power series spectrum.
Establishes existence and normality of the smallest lc center in dimension 3.
Applies results to the ACC for minimal log discrepancies > 1 on non-singular 3-folds.
Abstract
We study the connectedness of the non-subklt locus over the spectrum of a formal power series ring. In dimension 3, we prove the existence and normality of the smallest lc centre, and apply it to the ACC for minimal log discrepancies greater than 1 on non-singular 3-folds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Coding theory and cryptography