Mike Roth

activity

20002025

most citedSeshadri constants, Diophantine approximation, and Roth's Theorem for arbitrary varieties

57 citations · 127 across the 15 of their papers we have counts for

collaborators

Showing math.AGShow all

14 papers · 1 filter

math.AG2025

Reduced Čech complexes and computing higher direct images under toric maps

Mike Roth, Sasha Zotine

This paper has three main goals : (1) To give an axiomatic formulation of the construction of "reduced Čech complexes", complexes using fewer than the usual number of intersections…

math.AG2025

Homeomorphism type of the non-negative part of a complete toric variety

Mike Roth

In this note we show that the nonnegative part of a proper complex toric variety has the homeomorphism type of a sphere, and consequently that the nonnegative part has a natural st…

math.AG2024

Seshadri constants on $P^{1} \times P^{1}$ , and applications to the symplectic packing problem

Chris Dionne, Mike Roth

In this paper we compute the $r$ -point Seshadri constant on $P^{1} \times P^{1}$ for those line bundles where the answer might be expected to be governed by $(- 1)$ -curv…

math.AG2020

Codimension two integral points on some rationally connected threefolds are potentially dense

David McKinnon, Mike Roth

Let $V$ be a smooth, projective, rationally connected variety, defined over a number field $k$ , and let $Z \subset V$ be a closed subset of codimension at least two. In this paper,…

math.AG2017

Intersection multiplicity one for classical groups

Ivan Dimitrov, Mike Roth

In this paper we show that when $G$ is a classical semi-simple algebraic group, $B \subset G$ a Borel subgroup, and $X = G / B$ , t…

math.AG2013

An analogue of Liouville's Theorem and an application to cubic surfaces

David McKinnon, Michael Roth

We prove a strong analogue of Liouville's Theorem in Diophantine approximation for points on arbitrary algebraic varieties. We use this theorem to prove a conjecture of the first a…