On blowing up the weighted projective plane

Abstract

We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute the Cox ring in several cases. Moreover applications to the study of ${\overline{M}}_{0,n}$ are discussed.

arXiv comment19 pages

References in corpus (4)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space
• Some non-finitely generated Cox rings
• Asymptotic regularity of powers of ideals of points in a weighted projective plane
• Computing Cox rings

Cited by in corpus (15)

• On torus actions of higher complexity
• Mori Dream Spaces and blow-ups of weighted projective spaces
• Curves generating extremal rays in blowups of weighted projective planes
• Positivity of divisors on blown-up projective spaces, II
• Newton-Okounkov bodies and Toric Degenerations of Mori dream spaces via Tropical compactifications
• Hyperelliptic classes are rigid and extremal in genus two
• On the effective cone of ${\overline{\mathcal{M}}}_{g,n}$
• Birational geometry of moduli spaces of configurations of points on the line
• Projective and birational geometry of Grassmannians and other special varieties
• Reductive quotients of klt singularities
• A presentation for the Cox ring of ${\overline{M}}_{0,6}$
• New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric Surfaces
• Balanced complexes and effective divisors on ${\overline{M}}_{0,n}$
• Finite generation of Cox rings
• Higher-dimensional Losev-Manin spaces and their geometry