2016/09/12 by Domokos, M., Joó, Dániel
#14M25 (Primary) 05E40 (Secondary) 14L24 (Secondary) 16G20 (Secondary) 52B20 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1609.03618
It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, Bøgvad's conjecture holds for quiver polytopes of dimension at most four. In arbitrary dimension, the toric ideal of a compressed polytope is generated in degree two if the polytope has no neighbouring singular vertices. Furthermore, the toric ideal of a compressed polytope with at most one singular vertex has a quadratic Gröbner basis.