19 citations · 52 across the 8 of their papers we have counts for
10 papers
Lens spaces as dual complexes of Log Calabi-Yau pairs
Morgan V Brown
We demonstrate the construction of singular log Calabi-Yau -folds such that the dual complex of the boundary is homeomorphic to a Lens space from a log Calabi-Yau surface with a…
On the structure of the complement of skeleton
Morgan Brown, Jiachang Xu, Muyuan Zhang
We study the higher dimensional geometry of Berkovich spaces using virtual open disks, which are given by fibration of relative dimension . Inspired by birational geometry, we c…
The Dual Complex of a semi-log canonical Surface
Morgan V Brown
Semi-log canonical varieties are a higher-dimensional analogue of stable curves. They are the varieties appearing as the boundary of a log canonical pair , and also appe…
The Essential Skeleton of a product of degenerations
Morgan Brown, Enrica Mazzon
We study the problem of how the dual complex of the special fiber of an snc degeneration $\cX_R$ changes under products. We view the dual complex as a skeleton inside the Berkovich…
Chip-firing groups of iterated cones
Morgan V. Brown, Jackson S. Morrow, David Zureick-Brown
Let be a finite graph and let be the "th cone over " (i.e., the join of and the complete graph ). We study the asymptotic structure of the chip-firing grou…
A geometric characterisation of toric varieties
Morgan Brown, James McKernan, Roberto Svaldi +1
We prove a conjecture of Shokurov which characterises toric varieties using log pairs.
Rational Connectivity and Analytic Contractibility
Morgan Brown, Tyler Foster
Let k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We pro…
The McKay correspondence, tilting equivalences, and rationality
Morgan Brown, Ian Shipman
We consider the problem of comparing t-structures under the derived McKay correspondence and for tilting equivalences. We relate the t-structures using certain natural torsion theo…
Singularities of Cox Rings of Fano Varieties
Morgan V. Brown
Let be a smooth complete Fano variety over . We show that the Cox ring is Gorenstein with canonical singulari…
Big -ample Line Bundles
Morgan V Brown
A recent paper of Totaro develops a theory of -ample bundles in characteristic 0. Specifically, a line bundle on is -ample if for every coherent sheaf o…