2015/06/19 by Emilia Mezzetti, Mezzetti, Emilia, Rosa M. Miró-Roig +1 · 1 citation
Mathematics · #13E10 #14M25 #14N05 #14N15 #53A20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13E10 #msc:14M25 #msc:14N05 #msc:14N15 #msc:53A20
paper · pdf · doi:10.48550/arxiv.1506.05914
27 pages, 3 figures. Final version accepted for publication in Ann. Mat. Pura Appl
arxiv created 2016/01/26 · arxiv updated 2016/01/27
We compute the minimal and the maximal bound on the number of generators of a minimal smooth monomial Togliatti system of forms of degree d in n+1 variables, for any d≥ 2 and n≥ 2. We classify the Togliatti systems with number of generators reaching the lower bound or close to the lower bound. We then prove that if n=2 (resp n=2,3) all range between the lower and upper bound is covered, while if n≥ 3 (resp. n≥ 4) there are gaps if we only consider smooth minimal Togliatti systems (resp. if we avoid the smoothness hypothesis). We finally analyze for n=2 the Mumford-Takemoto stability of the syzygy bundle associated to smooth monomial Togliatti systems.