4 papers · 1 filter
Orbifold Degenerations of Hirzebruch Surfaces
Juan Pablo Zúñiga
We study orbifold degenerations of Hirzebruch surfaces. Our main theorem shows that every such degeneration arises as a partial smoothing of a toric surface. We then give a com…
Computing Cox rings via the cone conjecture
Tomoki Oda, José Ignacio Yáñez, Juan Pablo Zúñiga
We initiate a program to study the Cox ring of Calabi-Yau varieties, employing the notion of Morrison-Kawamata dream spaces. In this setting, we establish an analogue of the Hu-Kee…
Degenerations of cluster type varieties
Joaquín Moraga, Juan Pablo Zúñiga
We study degenerations of cluster type varieties and pairs. Our first theorem proves that degenerations of toric pairs are finite quotients of toric pairs. In a similar vein, under…
Wahl singularities in degenerations of del Pezzo surfaces
Giancarlo Urzúa, Juan Pablo Zúñiga
For any fixed , we characterize all Wahl singularities that appear in degenerations of del Pezzo surfaces of degree . This extends the work of Manetti and…