2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/199983Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure ρif a zero-order term ν_ρ is added to the Δoperator. The effects of this odd scalar term ν_ρ become relevant at two-loop order. We prove that ν_ρ is essentially the odd scalar curvature of an arbitrary torsion-free connection that is compatible with both the anti-Poisson structure E and the density ρ. This extends a previous result for non-degenerate antisymplectic manifolds to degenerate anti-Poisson manifolds that admit a compatible two-form.9 pages, LaTeX. v2: Minor changes. v3: Published versionHigh Energy Physics - TheoryMathematical PhysicsSymplectic Geometrytext