Abstract
AbstractWe study linear systems of surfaces in $${\mathbb {P}}^3$$
P
3
singular along general lines. Our purpose is to identify and classify special systems of such surfaces, i.e., those non-empty systems where the conditions imposed by the multiple lines are not independent. We prove the existence of four surfaces arising as (projective) linear systems with a single reduced member. Till now no such examples have been known. These are unexpected surfaces in the sense of recent work of Cook II, Harbourne, Migliore, and Nagel. It is an open problem if our list is complete, i.e., if it contains all reduced and irreducible unexpected surfaces based on lines in $${\mathbb {P}}^3$$
P
3
. As an application we find Waldschmidt constants of six general lines in $${\mathbb {P}}^3$$
P
3
and an upper bound for this invariant for seven general lines.
Publisher
Springer Science and Business Media LLC
Reference42 articles.
1. Aladpoosh, T.: Postulation of generic lines and one double line in $${\mathbb{P}}^{n}$$ in view of generic lines and one multiple linear space. Selecta Math. (N.S.) 25(1), # 9 (2019)
2. Alexander, J., Hirschowitz, A.: Polynomial interpolation in several variables. J. Algebraic Geom. 4(2), 201–222 (1995)
3. Bauer, Th., Di Rocco, S., Schmidt, D., Szemberg, T., Szpond, J.: On the postulation of lines and a fat line. J. Symblic Comput. 91, 3–16 (2019)
4. Bauer, Th., Malara, G., Szpond, J., Szemberg, T.: Quartic unexpected curves and surfaces. Manuscripta Math. 161(3–4), 283–292 (2020)
5. Bocci, C.: Special effect varieties in higher dimension. Collect. Math. 56(3), 299–326 (2005)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献