Seminormal log centers and deformations of pairs

TL;DR

This paper extends properties of log canonical centers to near-centers and demonstrates that deformations with coefficients above 1/2 avoid embedded points, with strengthened results from recent work.

Contribution

It introduces new properties of near log canonical centers and improves understanding of deformations with large coefficients, building on recent advances.

Findings

Properties of log canonical centers extend to near-centers.

Deformations with coefficients > 1/2 do not produce embedded points.

Results are strengthened using recent work of Birkar, Hacon, and Xu.

Abstract

We show that some properties of log canonical centers of a log canonical pair (X,D) also hold for certain subvarieties that are close to being a log canonical center. As a consequence, we obtain that if one works with deformations of pairs (X, D) where all the coefficients of D are bigger than 1/2, then one need not worry about embedded points on D. May 20: Results strengthened using recent work of Birkar and Hacon and Xu.