TY - JOUR

T1 - Corrigendum to “On the construction of weakly Ulrich bundles” [Adv. Math. 381 (2021) 107598](S0001870821000360)(10.1016/j.aim.2021.107598)

AU - Joshi, Kirti

N1 - Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2021

Y1 - 2021

N2 - 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=F⁎(ωXr+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].

AB - 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=F⁎(ωXr+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].

KW - Almost Ulrich bundles

KW - Surfaces of general type

KW - Ulrich bundles

KW - Weakly Ulrich bundles

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U2 - 10.1016/j.aim.2021.108025

DO - 10.1016/j.aim.2021.108025

M3 - Comment/debate

AN - SCOPUS:85118784763

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 108025

ER -