TY - JOUR
T1 - Basepoint-freeness thresholds and higher syzygies on abelian threefolds
AU - Ito, Atsushi
N1 - Funding Information:
Received 10 January 2021, accepted in final form 23 June 2022. 2020 Mathematics Subject Classification 14K05 (primary), 14C20 (secondary). Keywords: syzygy, abelian variety, basepoint-freeness threshold. This journal is © Foundation Compositio Mathematica 2022. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica. The author was supported by Grant-in-Aid for Scientific Research (17K14162).
Publisher Copyright:
© Foundation Compositio Mathematica 2022. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.
PY - 2022/11
Y1 - 2022/11
N2 - For a polarized abelian variety, Z. Jiang and G. Pareschi introduced an invariant and showed that the polarization is basepoint-free or projectively normal if the invariant is small. Their result was generalized to higher syzygies by F. Caucci; that is, the polarization satisfies property (Np) if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we armatively answer some questions on abelian varieties asked by the author, V. Lozovanu and F. Caucci in the three-dimensional case.
AB - For a polarized abelian variety, Z. Jiang and G. Pareschi introduced an invariant and showed that the polarization is basepoint-free or projectively normal if the invariant is small. Their result was generalized to higher syzygies by F. Caucci; that is, the polarization satisfies property (Np) if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we armatively answer some questions on abelian varieties asked by the author, V. Lozovanu and F. Caucci in the three-dimensional case.
KW - Abelian variety
KW - Basepoint-freeness threshold.
KW - Syzygy
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U2 - 10.14231/AG-2022-023
DO - 10.14231/AG-2022-023
M3 - Article
AN - SCOPUS:85141787251
SN - 2313-1691
VL - 9
SP - 762
EP - 787
JO - Algebraic Geometry
JF - Algebraic Geometry
IS - 6
ER -