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PreprintCC BY-NC-ND 4.0arXiv

Pushforwards of lc pairs under morphisms to abelian varieties

  • Fanjun Meng
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Abstract

Let f be a morphism from a log canonical pair (X,Δ) to an abelian variety A and D∼ℚm(KX+Δ) a Cartier divisor on X with m>1 a rational number. We prove that f*𝒪X(D) is globally generated after pullback by an isogeny. Our methods involve birational geometry, mixed Hodge modules and singular Hermitian metrics with the minimal extension property. Moreover, we provide simple counterexamples where the above result fails for plt pairs when m=1 and where the existence of Chen--Jiang decompositions fails for plt pairs for any m≥1.

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Cite

BibTeXRIS
BibTeX
@misc{meng2026pushforwards,
  title = {{Pushforwards of lc pairs under morphisms to abelian varieties}},
  author = {Fanjun Meng},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04801},
  eprint = {2611.04801},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04801},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Pushforwards of lc pairs under morphisms to abelian varieties
AU  - Fanjun Meng
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04801
UR  - https://arxiv.org/abs/2611.04801
AB  - Let f be a morphism from a log canonical pair (X,Δ) to an abelian variety A and D∼_ℚm(K_X+Δ) a Cartier divisor on X with m>1 a rational number. We prove that f_*𝒪_X(D) is globally generated after pullback by an isogeny. Our methods involve birational geometry, mixed Hodge modules and singular Hermitian metrics with the minimal extension property. Moreover, we provide simple counterexamples where the above result fails for plt pairs when m=1 and where the existence of Chen--Jiang decompositions fails for plt pairs for any m≥1.
ER  -