On the Hilbert function of lines union one non-reduced point

Abstract

Polito SFX(opens in a new window)| Export | Download | Add to List | More... Annali della Scuola normale superiore di Pisa - Classe di scienze Volume 15, 2016, Pages 69-84 On the Hilbert function of lines union one non-reduced point (Article) Carlini, E.a , Catalisano, M.V.bc , Geramita, A.V.d a Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca Degli Abbruzzi 24, Torino, Italy b DIME Dipartimento di Ingegneria Meccanica Energetica Gestionale E Dei Trasporti, Universita Degli Studi di Genova, Piazzale Kennedy pad. D, Genova, Italy c Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada View additional affiliations View references (18) Abstract In this paper we consider the problem of determining the Hilbert function of schemes XcP which are the generic union of s lines and one m- multiple point. We completely solve this problem for any s and m when n ≥ 4. When n = 3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.