2014/01/15 by Giuseppe Favacchio, Favacchio, Giuseppe, Alfio Ragusa +3
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.1401.3535
Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in ℙr as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are finite union of linear varieties whose support set is a suitable finite subset of ℤ+c called tower set. We prove that the tower schemes are arithmetically Cohen-Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen-Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes (in codimension 2) and we show that the support of these configurations (the generalized tower set) gives a combinatorial characterization of the primary decomposition of the arithmetically Cohen-Macaulay squarefree monomial ideals.