Tilt stability and the degree of irrationality of surfaces on threefolds

2019/07/30 by Smith, Geoffrey
#14C21 #14E08 (Primary) 14F05 #14J28 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.13084

Abstract

Let S be a smooth projective surface on a smooth threefold X such that X has Picard rank 1 and NS(S) is generated by the restriction of divisors from X. We show that if X satisfies the Bogomolov-Gieseker type inequality for tilt semistable objects conjectured by Bayer-Macrì-Stellari, then the minimum degree of a dominant rational map S\dashrightarrowℙ² is either relatively large or determined by a net of curves of low degree on S. As one application, we prove that the complete intersection of three very general quadrics in ℙ⁵ has degree of irrationality 4.

Related

• The degree of irrationality of most abelian surfaces is 4
• Irrationality of threefolds via Weil's conjectures
• Some examples of tilt-stable objects on threefolds
• Measures of irrationality of the Fano surface of a cubic threefold
• The Degree of Irrationality of del Pezzo Surfaces