Rational weighted projective hypersurfaces

2024/09/02 by Esser, Louis · 3 citations
#14E08 #14J70 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.01333

Abstract

A very general hypersurface of dimension n and degree d in complex projective space is rational if d ≤ 2, but is expected to be irrational for all n, d ≥ 3. Hypersurfaces in weighted projective space with degree small relative to the weights are likewise rational. In this paper, we introduce rationality constructions for weighted hypersurfaces of higher degree that provide many new rational examples over any field. We answer in the affirmative a question of T. Okada about the existence of very general terminal Fano rational weighted hypersurfaces in all dimensions n ≥ 6.

Cited by

• A survey on birational Rigidity of threefold Weighted Complete Intersections
• Weighted four-dimensional Fano hypersurfaces of K3 type
• Weighted surfaces with maximal Picard number

Related

• Rationality of weighted hypersurfaces of special degree
• Smooth weighted hypersurfaces that are not stably rational
• Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
• Some low-dimensional hypersurfaces that are not stably rational
• Stable rationality of orbifold Fano threefold hypersurfaces