Selection rules of canonical differential equations from Intersection theory

Abstract: The matrix of canonical differential equations consists of the 1-$\mathrm{d}\log$-form coefficients obtained by projecting ($n$+1)-$\mathrm{d}\log$-forms onto $n$-$\mathrm{d}\log$-form master integrands. With dual form in relative cohomology, the intersection number can be used to achieve the projection and provide the selection rules for canonical differential equations, which relate to the pole structure of the $\mathrm{d}\log$ master integrands.