Tootfinder

This https://arxiv.org/abs/2505.08752 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Three Tone Networks and a Tessellation
The Eulerian tonnetz, which associates three minor chords to each major chord and three major chords to each minor chord, can be represented by a bipartite graph with twelve white vertices signifying major chords and twelve black vertices signifying minor chords. This so-called Levi graph uniquely determines the combinatorial geometry of a remarkable configuration of twelve points and twelve lines in the real projective plane with the property that three points lie on each line and three lines …

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
Ana Pavlakovi\'c
https://arxiv.org/abs/2505.23531 https://

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane. As an application, conjectures regarding rationality and symmetry are supported by verification of a special case.

Quadratic Segre indices
Felipe Espreafico, Stephen McKean, Sabrina Pauli
https://arxiv.org/abs/2506.01547 https://arxiv.org/pdf/2506.…

Quadratic Segre indices
We prove that the local Euler class of a line on a degree $2n-1$ hypersurface in projective $n+1$ space is given by a product of indices of Segre involutions. Segre involutions and their associated indices were first defined by Finashin and Kharlamov over the reals. Our result is valid over any field of characteristic not 2 and gives an infinite family of problems in enriched enumerative geometry with a shared geometric interpretation for the local type.