The Only Complex 4-net is the Hesse Configuration

It has been conjectured that the only nets realizable in CP2 are 3-nets and the Hesse configuration (up to isomorphism). The goal of this talk will be to outline our proof, together with A. Bassa, of this conjecture. A preprint containing our results is available at arXiv:2002.02660.
Arrangements at Home II: Cohomology Jump Loci


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Nakiboğlu, Barış (2017-08-25)
For any channel with a convex constraint set and finite Augustin capacity, existence of a unique Augustin center and associated Erven-llarremoes bound are established. Augustin-Legendre capacity, center, and radius are introduced and proved to be equal to the corresponding Renyi-Gallager entities. Sphere packing bounds with polynomial prefactors are derived for codes on two families of channels: (possibly non-stationary) memoryless channels with multiple additive cost constraints and stationary memoryless c...
The property of smallness up to a complemented Banach subspace
Abdeljawad, T; Yurdakul, Murat Hayrettin (2004-04-01)
This article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not sa...
The second homology groups of mapping class groups of orientable surfaces
Korkmaz, Mustafa (Cambridge University Press (CUP), 2003-05-01)
Let $\Sigma_{g,r}^n$ be a connected orientable surface of genus $g$ with $r$ boundary components and $n$ punctures and let $\Gamma_{g,r}^n$ denote the mapping class group of $\Sigma_{g,r}^n$, namely the group of isotopy classes of orientation-preserving diffeomorphisms of $\Sigma_{g,r}^n$ which are the identity on the boundary and on the punctures. Here, we see the punctures on the surface as distinguished points. The isotopies are required to be the identity on the boundary and on the punctures. If $r$ and...
The class of (1,3)-groups with homocyclic regulator quotient of exponent p(4) has bounded representation type
Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (Elsevier BV, 2014-02-15)
The class of almost completely decomposable groups with a critical typeset of type (1,3) and a homocyclic regulator quotient of exponent p(4) is shown to be of bounded representation type. There are only nine near-isomorphism types of indecomposables, all of rank <= 6.
Self-dual Yang-Mills fields in eight dimensions
Bilge, AH; Dereli, T; Kocak, S (Springer Science and Business Media LLC, 1996-03-01)
Strongly self-dual Yang-Mills fields in even-dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields F-mu nu. We derive a topological bound on R(8), integral(M)(F, F)(2) greater than or equal to k integral(M) p(1)(2), where p(1) is the first Pontryagin class of the SO(n) Yang-Mills bundle, and k is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.
Citation Formats
A. U. Ö. Kişisel, “The Only Complex 4-net is the Hesse Configuration,” presented at the Arrangements at Home II: Cohomology Jump Loci, Ontario, Kanada, 2020, Accessed: 00, 2021. [Online]. Available: