Examples of non--effective rays at the boundary of the Mori cone of\n blow--ups of the plane

2021/11/04 by Ciro Ciliberto, Ciliberto, Ciro, Rick Miranda +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2111.02920

openalex publication_date 2021/11/04 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that no multiple of the linear system of plane curves\nof degree d\≥ 4 with a point of multiplicity d-m (with 2 \≤ m \≤ d)\nand m(2d-m) simple general points is effective.\n

Related

• Non effective planar linear systems at the boundary of the Mori cone
• On the Mori cone of blow-ups of the plane
• Irrational nef rays at the boundary of the Mori cone for very general blowups of the plane
• Variations on Nagata's Conjecture
• Double Points of Plane Models in M_g,1