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Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM

  • Felix Janda
  • Ruoxi Li
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Abstract

Many perfect obstruction theories and virtual cycles in enumerative geometry are shadows from derived geometry. In this paper, we give a general construction of reduced perfect obstruction theories arising from a geometric reduction of the derived stack X with respect to a (−1)-shifted log function wα. Notably, this construction leads to a decomposition of the virtual cycle [X]vir into the reduced virtual cycle [X]red and a reduced boundary cycle [ΔX]red. Our construction is motivated by future applications to the moduli stack of UMD logarithmic R-maps in log GLSM \cite{CJR21}. Along the way, we develop logarithmic analogs of several constructions in derived geometry, in particular proving a logarithmic Lagrangian intersection theorem.

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Cite

BibTeXRIS
BibTeX
@misc{janda2026delignefaltings,
  title = {{Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM}},
  author = {Felix Janda and Ruoxi Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23803},
  eprint = {2610.23803},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23803},
}
RIS
TY  - UNPB
TI  - Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM
AU  - Felix Janda
AU  - Ruoxi Li
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23803
UR  - https://arxiv.org/abs/2610.23803
AB  - Many perfect obstruction theories and virtual cycles in enumerative geometry are shadows from derived geometry. In this paper, we give a general construction of reduced perfect obstruction theories arising from a geometric reduction of the derived stack X with respect to a (−1)-shifted log function w_α. Notably, this construction leads to a decomposition of the virtual cycle [X]^vir into the reduced virtual cycle [X]^red and a reduced boundary cycle [Δ_X]^red. Our construction is motivated by future applications to the moduli stack of UMD logarithmic R-maps in log GLSM \cite{CJR21}. Along the way, we develop logarithmic analogs of several constructions in derived geometry, in particular proving a logarithmic Lagrangian intersection theorem.
ER  -