6 papers
Euclidean -systems and real PK arrangements
Martin de Borbon, Dmitri Panov, Alexander P. Veselov
We establish a correspondence between two structures arising in the geometry of hyperplane arrangements: Euclidean -systems and real polyhedral Kähler (PK) arrangements. We p…
The Hirzebruch quadratic form of a hyperplane arrangement and flat logarithmic connections
Martin de Borbon, Dmitri Panov
We prove that the Hirzebruch quadratic form of a complex hyperplane arrangement is non-positive on the set of stable weights, and we identify the zero locus within this set with fl…
A Miyaoka-Yau inequality for hyperplane arrangements in
Martin de Borbon, Dmitri Panov
Let be a hyperplane arrangement in . We define a quadratic form on that is entirely determined by the intersection poset…
Polyhedral Kähler metrics on
Martin de Borbon, Dmitri Panov
We give necessary and sufficient conditions for the existence of polyhedral Kähler metrics on whose singular set is a hyperplane arrangement and whose cone angles…
Microscopic structure of the vortex cores in granular niobium: A coherent quantum puzzle
V. S. Stolyarov, V. Neverov, A. V. Krasavin +12
When macroscopic quantum condensates -- superconductors, superfluids, cold atoms and ions, polaritons etc. -- are put in rotation, a quantum vortex lattice forms inside. In homogen…
Simplicial arrangements with few double points
Dmitri Panov, Guillaume Tahar
In their solution to the orchard-planting problem, Green and Tao established a structure theorem which proves that in a line arrangement in the real projective plane with few doubl…