8 citations · 31 across the 20 of their papers we have counts for
25 papers
The relation type of point configurations in the projective plane
Ethan Cotterill, Amir Mohammad Kach khaali, Abbas Nasrollah Nejad
We study the {\it relation type} of ideals of finite reduced sets of points in the projective plane; for a given ideal, this is the maximal -degree of a minimal generator of the…
On gap sets in arbitrary Kummer extensions of
Ethan Cotterill, Erik A. R. Mendoza, Pietro Speziali
Let be an algebraically closed field, and let be a Kummer extension of function fields of genus . We provide a compact and explicit description of the gap set $G(Q)…
Matroids and semirings attached to toric singularity arrangements
Ethan Cotterill, Cristhian Garay López
Curve singularities are classical objects of study in algebraic geometry. The key player in their combinatorial structure is the {\it value semigroup}, or its compactification, the…
Cusps in with prescribed ramification
Ethan Cotterill, Nathan Kaplan, Renata Vieira Costa
We study value semigroups associated to germs of maps with fixed ramification profiles in a distinguished point. We then apply our analysis to…
Towards Brill--Noether theory for cuspidal curves
Ethan Cotterill, Renato Vidal Martins
Understanding when an abstract complex curve of given genus comes equipped with a map of fixed degree to a projective space of fixed dimension is a foundational question; and Brill…
Certified Severi dimensions for hyperelliptic and supersymmetric cusps
Ethan Cotterill, Vinícius Lima, Renato Vidal Martins +1
In a previous paper, the first three authors formulated a precise conjecture about the dimension of the {\it generalized Severi variety} of degree-…