2017/02/01 by Askold Khovanskiĭ, Khovanskii, Askold, Leonid Monin +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1702.00470
openalex publication_date 2017/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let RΔ(f1,…,fn+1) be the \it Δ-resultant (see below) of (n+1)-tuple of Laurent polynomials. We provide an algorithm for computing RΔ assuming that an n-tuple (f2,…,fn+1) is \it developed (see sec.6). We provide a relation between the product of f1 over roots of f2=…=fn+1=0 in (\mathbb C^*)n and the product of f2 over roots of f1=f3=…=fn+1=0 in (\mathbb C^*)n assuming that the n-tuple (f1f2,f3,…,fn+1) is developed. If all n-tuples contained in (f1,…,fn+1) are developed we provide a signed version of Poisson formula for RΔ. In our proofs we use a topological arguments and topological version of the Parshin reciprocity laws.