15 citations · 28 across the 4 of their papers we have counts for
5 papers
A bound on embedding dimensions of geometric generic fibers
Zachary Maddock
We limit the singularities that arise in geometric generic fibers of morphisms between smooth varieties of positive characteristic by studying changes in embedding dimension under…
Regular del Pezzo surfaces with irregularity
Zachary Maddock
We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We al…
A ratio of integration between quotients in geometric invariant theory
Zachary Maddock
Let T be a maximal torus of a connected reductive group G that acts linearly on a projective variety X so that all semi-stable points are stable. This paper compares the integratio…
Level Sets of the Takagi Function: Generic Level Sets
Jeffrey C. Lagarias, Zachary Maddock
The Takagi function τ : [0, 1] \rightarrow [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. This paper studies the level sets L(y) = {x : τ(x) = y}…
Level Sets of the Takagi Function: Local Level Sets
Jeffrey C. Lagarias, Zachary Maddock
The Takagi function τ: [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : τ(x) = y} of the Takagi function τ(x)…