Arithmetic statistics on cubic surfaces

R Das - Research in the Mathematical Sciences, 2020 - Springer
In this paper, we compute the distributions of various markings on smooth cubic surfaces
defined over the finite field F _q F q, for example the distribution of pairs of points,'tritangents' …

Problems in arithmetic topology

C Gómez-Gonzáles, J Wolfson - Research in the Mathematical Sciences, 2021 - Springer
We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF
workshop on “Arithmetic Topology.” Three problem sessions were hosted during the …

Classification of singular del Pezzo surfaces over finite fields

R Blache, E Hallouin - Mathematische Zeitschrift, 2023 - Springer
In this article, we consider weak del Pezzo surfaces defined over a finite field, and their
associated, singular, anticanonical models. We first define arithmetic types for such surfaces …

Cohomology of complements of Toric arrangements associated to root systems

O Bergvall - arXiv preprint arXiv:1601.01857, 2016 - arxiv.org
We compute the cohomology of the complement of toric arrangements associated to root
systems as representations of the corresponding Weyl groups. Specifically, we develop an …

Arithmetic and topology of classical structures associated with plane quartics

O Bergvall - European Journal of Mathematics, 2023 - Springer
We consider moduli spaces of plane quartics marked with various structures such as Cayley
octads, Aronhold heptads, Steiner complexes and Göpel subsets and determine their …

Configurations of noncollinear points in the projective plane

R Das, B O'Connor - Algebraic & Geometric Topology, 2021 - msp.org
We consider the space F n of configurations of n points in ℙ 2 satisfying the condition that no
three of the points lie on a line. For n= 4, 5, 6, we compute H∗(F n; ℚ) as an 𝔖 n …

On the cohomology of the space of seven points in general linear position

O Bergvall - Research in Number Theory, 2020 - Springer
We determine the cohomology groups of the space of seven points in general linear position
in the projective plane as representations of the symmetric group on seven elements by …

Cohomology of complements of toric arrangements associated with root systems

O Bergvall - Research in the Mathematical Sciences, 2022 - Springer
We develop an algorithm for computing the cohomology of complements of toric
arrangements. In the case a finite group Γ Γ is acting on the arrangement, the algorithm …

Frobenius actions on Del Pezzo surfaces of degree 2

O Bergvall - … in Incidence Geometry: Algebraic, Topological and …, 2024 - msp.org
We determine the number of Del Pezzo surfaces of degree 2 over finite fields of odd
characteristic with specified action of the Frobenius endomorphism, ie, we solve the …

Algebraic & Geometric

Z LI - Algebraic & Geometric Topology, 2021 - projecteuclid.org
Heegaard Floer homology is a package of invariants of 3–manifolds invented by Ozsváth
and Szabó, using holomorphic disks and Heegaard splittings of the 3–manifold [13; 12]. It …