Open AccessInterpolation on surfaces in ℙ³
Author(s) -
Jack Huizenga
Publication year - 2012
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2012-05582-6
Subject(s) - algorithm , annotation , computer science , artificial intelligence
Suppose S S is a surface in P 3 \mathbb {P}^3 , and p 1 , … , p r p_1,\ldots ,p_r are general points on S S . What is the dimension of the space of sections of O S ( e ) \mathcal {O}_S(e) having singularities of multiplicity m i m_i at p i p_i for all i i ? We formulate two natural conjectures which would answer this question, and we show they are equivalent. We then prove these conjectures in case all multiplicities are at most 4 4 .