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math.AG2026

Higher Du Bois and Higher Rational Pairs

Haoming Ning, Brian Nugent

We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, incl…

math.AG2025

Moduli of Very Ample Line Bundles

Brian Nugent

Let be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on . In doing so, we develop a generalization of Fitting…