Corrigendum: “On the construction of weakly Ulrich bundles” (Advances in Mathematics (2021) 381, (107598), (S0001870821000360), (10.1016/j.aim.2021.107598))

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Abstract

This note corrects a mistake in [3, Theorem 4.1]. The error noted here does not affect any other results of [3]. To correct the error, here I prove a more general result (Theorem 3.1) and deduce Theorem 3.3 and also the correct version of the previously announced theorem in Theorem 3.4. Theorem 3.5 supplements Theorem 3.3. In it, I prove that if k is an algebraically closed field of characteristic p≥3 and X/k is any smooth, projective, minimal surface of general type and with Pic(X)=Z, then for all integers r≥5, X is embedded as a smooth surface by its pluricanonical linear system X↪|ωXr|, and E=FXr+1)(1) is an almost Ulrich bundle for the pluricanonical embedding X↪|ωXr| of X and for the ample line bundle provided by this embedding. Corollary 3.6 generalizes [3, Theorem 3.1].

Original languageEnglish (US)
Article number108025
JournalAdvances in Mathematics
Volume394
DOIs
StatePublished - Jan 22 2022

Keywords

  • Almost Ulrich bundles
  • Surfaces of general type
  • Ulrich bundles
  • Weakly Ulrich bundles

ASJC Scopus subject areas

  • Mathematics(all)

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