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math.AG2025
b-divisorial valuations and Berkovich positivity functions
Joaquim Roé, Stefano Urbinati
We prove semicontinuity properties for local positivity invariants of big and nef divisors. The usual definition of Seshadri constant and asymptotic order of vanishing along a subv…
math.AG2025
Boundedness Results for Planar Linear Systems Assuming The Segre-Harbourne-Gimigliano-Hirschowitz Conjecture
Ciro Ciliberto, Rick Miranda, Joaquim Roé
Let be the projective plane blown up at general points. In this paper we give several consequences of the Segre-Harbourne-Gimigliano-Hirschowitz Conjecture, that…
math.AG2023
Quadric cones on the boundary of the Mori cone for very general blowups of the plane
Ciro Ciliberto, Rick Miranda, Joaquim Roé
We show the existence of cones over 8-dimensional rational spheres at the boundary of the Mori cone of the blow-up of the plane at very general points. This gives eviden…