# Sparse* *singularities

Algebraic geometry

## Sparse curve singularities, singular loci of resultants, and Vandermonde matrices

Submitted (2023)

Singularities, such as cusps or self-intersections, are points where mathematical objects such as functions or surfaces cease to be well-behaved. Extensively studied, important examples of these points can, intriguingly, be described by polynomials with indeterminate coefficients. We deduce some general results for singularities of this form, including a formula for the delta invariant, an index of their complexity.

Submitted (2023)