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PreprintCC BY-NC-ND 4.0arXiv

Generic vanishing conjecture for divisors

  • Fanjun Meng
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Abstract

Generic vanishing conjecture proposed by Pareschi and Popa is about the relationship between the existence of subvarieties of codimension >1 of principally polarized abelian varieties representing minimal cohomology class and the positivity of their ideal sheaves twisted by the principal polarization. Inspired by their formulation, we prove a codimension $1$ analog of generic vanishing conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{meng2026generic,
  title = {{Generic vanishing conjecture for divisors}},
  author = {Fanjun Meng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11377},
  eprint = {2609.11377},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11377},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Generic vanishing conjecture for divisors
AU  - Fanjun Meng
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11377
UR  - https://arxiv.org/abs/2609.11377
AB  - Generic vanishing conjecture proposed by Pareschi and Popa is about the relationship between the existence of subvarieties of codimension >1 of principally polarized abelian varieties representing minimal cohomology class and the positivity of their ideal sheaves twisted by the principal polarization. Inspired by their formulation, we prove a codimension $1$ analog of generic vanishing conjecture.
ER  -