2021/09/17 by Avinash Kulkarni, Kulkarni, Avinash, Sameera Vemulapalli +1
Computer Science · Mathematics · #14H10 (secondary) #14M12 (primary) #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2109.08740
openalex publication_date 2021/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From a block-diagonal (n+1) × (m+1) × (m+1) tensor symmetric in the last two entries one obtains two varieties: an intersection of symmetric determinantal hypersurfaces X in n-dimensional projective space, and an intersection of quadrics \mathfrakC in m-dimensional projective space. Under mild technical assumptions, we characterize the accidental singularities of X in terms of \mathfrakC. We apply our methods to algebraic curves and show how to construct theta characteristics of certain canonical curves of genera 3, 4, and 5, generalizing a classical construction of Cayley.