Two rational nodal quartic threefolds

2015/11/23 by Cheltsov, Ivan, Shramov, Constantin
#14E05 #14E08 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.07508

Abstract

We prove that the quartic threefolds defined by ∑_i=0⁵x_i=∑_i=0⁵x_i⁴-t(∑_i=0⁵x_i²)²=0 in ℙ⁵ are rational for t=(1)/(6) and t=(7)/(10).

Related

• Non-rational nodal quartic threefolds
• A very general quartic double fourfold or fivefold is not stably rational
• Q-factorial quartic threefolds
• Double covers of smooth quadric threefolds with Artin-Mumford obstructions to rationality
• Non-rationality of the S₆-symmetric quartic threefolds