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arXiv · 2007.05267

Steiner systems and configurations of points

Edoardo Ballico·Giuseppe Favacchio·Elena Guardo·Lorenzo Milazzo
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Abstract

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S(t,n,v)$ we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement.

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Edoardo Ballico, Giuseppe Favacchio, Elena Guardo, Lorenzo Milazzo. 2020-07-10. Steiner systems and configurations of points. https://arxiv.org/abs/2007.05267

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