Images of Rational Maps of Projective Spaces

2013/10/31 by Binglin Li, Li, Binglin · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AC #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1310.8453

31 pages

arxiv created 2013/10/31 · openalex publication_date 2013/10/31 · arxiv updated 2013/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the closure of the image of the rational map using a combination of techniques of moduli functors and initial degenerations. We first give a formula of multi-degree in terms of the dimensions of intersections of linear subspaces and then prove that it is Cohen-Macaulay. Finally, we compute its Hilbert polynomials.

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• Vanishing theorems for combinatorial geometries
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• The geometry of zonotopal algebras II: Orlik--Terao algebras and Schubert varieties

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