Relative Logarithmic AKSZ Descent on Joyce Generalized Corners
Abstract
We study resolution-independent relative logarithmic source complexes for AKSZ-BV-BFV theory on face-oriented Joyce manifolds with generalized corners. Under the geometric hypotheses (G1)-(G3), the Dupont-Panzer-Pym total relative logarithmic complexes of admitted smooth monoidal resolutions represent j!ΩX∘• and carry the same compactly supported derived trace. The comparison is deliberately unfiltered: it identifies total relative cocycle classes through the common interior, but not individual resolved faces, separate BFV descendants, nonlinear mapping spaces, or absolute regularized integrals. For the intrinsic b-source bT[1]X we formulate the additional Stokes and transfer data needed to recover strict facewise structures. A multiplicative regularized Stokes trace system on Joyce's face category gives the presymplectic intrinsic BV-BFV identity and incidence descent. The finite datum (G4) is a linear subdivision/aggregation transfer criterion; (G5) is a separate cyclic field-level criterion for classical abelian BF theory. Neither is a general existence theorem, and no general strict multiplicative intrinsic trace is constructed here. We prove the interval contractions needed for codimension-two collars and analyze the positive real conifold through the common star refinement of its two diagonal resolutions. On an explicit finite product-Whitney logarithmic class the exceptional square satisfies (G4) after normal-face totalization, and the transferred differential is exactly the signed intrinsic incidence differential. Its finite algebraic BF dual gives a cyclic logarithmic-cellular shadow, but not the full continuum intrinsic b-de Rham datum (G5). General nonlinear continuum pushforward, existence of the intrinsic multiplicative trace, and loop-level logarithmic graph integrals remain open.
Related
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BibTeX
@misc{anghel2026relative,
title = {{Relative Logarithmic AKSZ Descent on Joyce Generalized Corners}},
author = {Cristian Anghel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27799},
eprint = {2609.27799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relative Logarithmic AKSZ Descent on Joyce Generalized Corners
AU - Cristian Anghel
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27799
UR - https://arxiv.org/abs/2609.27799
AB - We study resolution-independent relative logarithmic source complexes for AKSZ-BV-BFV theory on face-oriented Joyce manifolds with generalized corners. Under the geometric hypotheses (G1)-(G3), the Dupont-Panzer-Pym total relative logarithmic complexes of admitted smooth monoidal resolutions represent j_!Ω_X^∘^• and carry the same compactly supported derived trace. The comparison is deliberately unfiltered: it identifies total relative cocycle classes through the common interior, but not individual resolved faces, separate BFV descendants, nonlinear mapping spaces, or absolute regularized integrals. For the intrinsic b-source ^bT[1]X we formulate the additional Stokes and transfer data needed to recover strict facewise structures. A multiplicative regularized Stokes trace system on Joyce's face category gives the presymplectic intrinsic BV-BFV identity and incidence descent. The finite datum (G4) is a linear subdivision/aggregation transfer criterion; (G5) is a separate cyclic field-level criterion for classical abelian BF theory. Neither is a general existence theorem, and no general strict multiplicative intrinsic trace is constructed here. We prove the interval contractions needed for codimension-two collars and analyze the positive real conifold through the common star refinement of its two diagonal resolutions. On an explicit finite product-Whitney logarithmic class the exceptional square satisfies (G4) after normal-face totalization, and the transferred differential is exactly the signed intrinsic incidence differential. Its finite algebraic BF dual gives a cyclic logarithmic-cellular shadow, but not the full continuum intrinsic b-de Rham datum (G5). General nonlinear continuum pushforward, existence of the intrinsic multiplicative trace, and loop-level logarithmic graph integrals remain open.
ER -