English

Quartic unexpected curves and surfaces

Algebraic Geometry 2018-04-11 v1 Commutative Algebra

Abstract

Our research is motivated by recent work of Cook II, Harbourne, Migliore, and Nagel on configurations of points in the projective plane with properties that are unexpected from the point of view of the postulation theory. In this note, we revisit the basic configuration of nine points appearing in work of Gennaro/Ilardi/Vall\`es and Harbourne, and we exhibit some additional new properties of this configuration. We then pass to projective three-space and exhibit a surface with unexpected postulation properties there. Such higher dimensional phenomena have not been observed so far.

Keywords

Cite

@article{arxiv.1804.03610,
  title  = {Quartic unexpected curves and surfaces},
  author = {Thomas Bauer and Grzegorz Malara and Tomasz Szemberg and Justyna Szpond},
  journal= {arXiv preprint arXiv:1804.03610},
  year   = {2018}
}

Comments

8 pages, 1 figure

R2 v1 2026-06-23T01:19:33.660Z