Open AccessOn the Hilbert function of lines union one non-reduced point
Author(s) -
Enrico Carlini,
Maria Virginia Catalisano,
Anthony V. Geramita
Publication year - 2016
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.201309_001
Subject(s) - function (biology) , point (geometry) , mathematics , pure mathematics , geometry , biology , genetics
We consider the problem of determining the Hilbert\udfunction of projective schemes X which are \udthe generic union of s lines and one m-multiple point.\udWe completely solve this problem for any s and m when n >3.\udWhen n=3 we find several defective such schemes and conjecture\udthat they are the only ones. We verify this conjecture in several\udcases