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' …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
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 …
and Szabó, using holomorphic disks and Heegaard splittings of the 3–manifold [13; 12]. It …