36 citations · 113 across the 18 of their papers we have counts for
24 papers
Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture
Patrick Brosnan
Motivated by Markman's work and by Kontsevich's tropical approach to disproving the Hodge conjecture, this note explains why families of Weil type abelian 2n-folds only have maxima…
Volumes of definable sets in o-minimal expansions and affine GAGA theorems
Patrick Brosnan
In this mostly expository note, I give a very quick proof of the definable Chow theorem of Peterzil and Starchenko using the Bishop-Stoll theorem and a volume estimate for definabl…
Fixed points, local monodromy, and incompressibility of congruence covers
Patrick Brosnan, Najmuddin Fakhruddin
We prove a fixed point theorem for the action of certain local monodromy groups on étale covers and use it to deduce lower bounds in essential dimension. In particular, we give mor…
Essential dimension in mixed characteristic
Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli
Suppose is a finite group and is either a prime number or . For positive, we say that is weakly tame at if has no non-trivial normal -subgroups. By co…
Jumps in the Archimedean Height
Patrick Brosnan, Gregory Pearlstein
We introduce a pairing on local intersection cohomology groups of variations of pure Hodge structure, which we call the asymptotic height pairing. Our original application of this…
Perverse obstructions to flat regular compactifications
Patrick Brosnan
Suppose is a smooth, proper morphism over a variety contained as a Zariski open subset in a smooth, complex variety . The goal of this note is to consider th…