Year: 2025
Type: article
Abstract: Let X be a rational surface obtained by blowing up at a configuration $$\mathscr {C}$$ C of infinitely near points over a Hirzebruch surface $$\mathbb {F}_\delta $$ F δ . We prove that there exist two positive integers $$a \le b$$ a ≤ b such that the cone of curves of X is finite polyhedral and minimally generated when $$\delta \ge a$$ δ ≥ a , and the Cox ring of X is finitely generated whenever $$\delta \ge b$$ δ ≥ b . The integers a and b depend only on a combinatorial object (a graph decorated with arrows) representing the strict transforms of the exceptional divisors, their intersections and those with the fibers and special section of $$\mathbb {F}_\delta $$ F δ .
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
OpenAlex ID: W4412362732