2021/07/09 by Kuei-Nuan Lin, Lin, Kuei-Nuan, Yi-Huang Shen +1 · 1 citation
Mathematics · Medicine · #13A30 #13F50 #13P10 #14M12 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Phytoestrogen effects and research #Primary 13C40 #Secondary 14N07 #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2107.04168
openalex publication_date 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we are mainly concerned with the blow-up algebras of the secant varieties of balanced rational normal scrolls. In the first part, we give implicit defining equations of their associated Rees algebras and fiber cones. Consequently, we can tell that the fiber cones are Cohen--Macaulay normal domains. Meanwhile, these fiber cones have rational singularities in characteristic zero, and are F-rational in positive characteristic. The Gorensteinness of the fiber cones can also be characterized. In the second part, we compute the Castelnuovo--Mumford regularities and a-invariants of the fiber cones. We also present the reduction numbers of the ideals defined by the secant varieties.