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arXiv · 2610.23803

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 $w_α$. Notably, this construction leads to a decomposition of the virtual cycle $[X]^{\mathrm{vir}}$ into the reduced virtual cycle $[X]^{\mathrm{red}}$ 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.

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BibTeXRIS

Felix Janda, Ruoxi Li. 2026-10-16. Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM. https://arxiv.org/abs/2610.23803

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