High-rank ternary forms of even degree

2017/06/14 by Alessandro De Paris, De Paris, Alessandro · 1 citation
Mathematics · #13P99 #14N15 #15A21 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1706.04604

openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit, for each even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives the lower bound \operatornamer_max(3,d)≥\lfloor\fracd²+2d+54\rfloor for d≥ 2, where \operatornamer_max(n,d) denotes the maximum rank of degree d forms in n variables with coefficients in an algebraically closed field of characteristic zero.

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