41 citations · 69 across the 10 of their papers we have counts for
6 papers · 1 filter
Resolving toric varieties with Nash blow-ups
Atanas Atanasov, Christopher Lopez, Alexander Perry +2
It is a long-standing question whether an arbitrary variety is desingularized by finitely many normalized Nash blow-ups. We consider this question in the case of a toric variety. W…
A survey of hypertoric geometry and topology
Nicholas J. Proudfoot
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the r…
All the GIT quotients at once
Nicholas J. Proudfoot
Let T be an algebraic torus acting on a smooth variety V. We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V.
A nonhausdorff model for the complement of a complexified arrangement
Nicholas J. Proudfoot
Given a hyperplane arrangement A in a real vector space, we introduce a real algebraic prevariety Z(A), and exhibit the complement of the complexification of A as the total space o…
Hyperkahler analogues of Kahler quotients
Nicholas J. Proudfoot
Let X be a Kahler manifold that is presented as a Kahler quotient of C^n by the linear action of a compact group G. We define the hyperkahler analogue M of X as a hyperkahler quoti…
Hyperpolygon spaces and their cores
Megumi Harada, Nicholas J. Proudfoot
Given an n-tuple of positive real numbers, Konno defines an algebraic variety called a hyperpolygon space, a hyperkahler analogue of the Kahler variety parametrizing spacial polygo…