Abstract
A common strategy in commutative algebra and algebraic geometry for studying algebraic varieties is to construct invariants that measure the complexity of their singularities. In characteristic zero, a prominent collection of these invariants includes multiplier ideals, their jumping numbers, and the Bernstein-Sato polynomial. In positive characteristic, their counterparts are test ideals, their F-jumping numbers, and Bernstein-Sato roots. Although these two families arise from very different origins, there is a close interaction between them. One of the most profound formulations of this connection is a conjecture predicting that multiplier ideals and test ideals essentially capture the same information.
In this work, we focus on quasi-homogeneous plane curves defined over fields of positive characteristic, along with their deformations at constant Milnor number. For an infinite number of primes, we give a complete description of their test ideals, F-jumping numbers, and Bernstein-Sato roots. Comparing them with the already known multiplier ideals, we verify that the reductions of these modulo a prime coincide with the test ideals.