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Bibliographic Details
Main Authors: Bini, Gilberto, Brambilla, Maria Chiara, Fontanari, Claudio, Postinghel, Elisa
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.14553
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Table of Contents:
  • Let $\overline{\mathrm{Mov}}^k(X)$ be the closure of the cone $\mathrm{Mov}^k(X)$ generated by classes of effective divisors on a projective variety $X$ with stable base locus of codimension at least $k+1$. We propose a generalized version of the Log Nonvanishing Conjecture and of the Log Abundance Conjecture for a klt pair $(X,Δ)$, that is: if $K_X+Δ\in \overline{\mathrm{Mov}}^{k}(X)$, then $K_X+Δ\in \mathrm{Mov}^{k}(X)$. Moreover, we prove that if the Log Minimal Model Program, the Log Nonvanishing, and the Log Abundance hold, then so does our conjecture.