Rationality of weighted hypersurfaces of special degree

2023/08/10 by Chitayat, Michael · 1 citation
#13A02 #14J26 #14M20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.05324

Abstract

Let X ⊂ ℙ(w₀, w₁, w₂, w₃) be a quasismooth well-formed weighted projective hypersurface and let L = lcm(w₀,w₁,w₂,w₃). We characterize when X is rational under the assumption that L divides deg(X) by combining an algebraic proof of rationality valid in all dimensions with a new result on numerical semigroups. As applications, we give new examples of families of normal projective rational varieties with quotient singularities and ample canonical divisor; we also determine precisely which affine Pham-Brieskorn threefolds are rational.

Cited by

• Weighted surfaces with maximal Picard number

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