Deligne pairing for equidimensional morphisms
Deligne pairing for equidimensional morphisms
Let $S$ be a noetherian normal scheme, and let $X\to S$ be a surjective projective morphism of pure relative dimension $d$. We construct a symmetric multi-additive functor $\mathcal{P}\mathrm{ic}(X)^{d+1} \to \mathcal{P}\mathrm{ic}(S)$, and prove its functorial properties. Our construction uses Elkik's and Garc\'ia's ideas, as well as algebraic Hartogs' theorem. Moreover, our …