arXiv subjects

Caroline Namanya

Publications and source records attributed to Caroline Namanya.

3 recordsLinked to original sources

arXiv2026

Group Actions from Algebraic Flops

This paper constructs derived autoequivalences associated to an algebraic flopping contraction X --> X_con, where X is quasi-projective with only mild singularities. These functors are constructed naturally using bimodule cones, and we prove these cones are locally two-sided tilting complexes by using the local-global properties and a key commutative diagram. The main result is that these autoequivalences combine to give an action of the fundamental group of an associated infinite hyperplane arrangement on the derived category of X. This generalises and simplifies \cite{DW3}, by finally removing reliance on subgroups, and it also lifts many other results from the complete local setting.

math.AG↗

arXiv2026

Finite automorphism groups of hypersurfaces via Bott vanishing

We give a cohomological criterion for the automorphism group scheme of a hypersurface in a smooth Deligne-Mumford stack to be discrete in tame characteristics. The criterion converts Bott-type vanishing on the ambient stack into vanishing of infinitesimal automorphisms of every quasismooth hypersurface in a linear system. We apply it to toric orbifolds, obtain uniform finiteness results for quasismooth weighted-projective hypersurfaces in tame characteristic and hypersurfaces in products of projective spaces, and identify the precise exceptional windows in which the method fails.

math.AG↗

arXiv2023

Pure Braid Group Presentations via Longest Elements

This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or certain palindromic length 5 box relations. This presentation is motivated by twist functors in algebraic geometry, but the proof is entirely Coxeter-theoretic. We also prove that the analogous set does not generate for all Coxeter arrangements, which in particular answers a question of Donovan and Wemyss.

math.GR↗