# The interpolation problem for a set of three fat points in $\mathbb{P}^1\times\mathbb{P}^1$

## TL;DR

This paper explicitly describes the minimal bigraded free resolution and Hilbert function for three fat points supported on an almost complete intersection in , solving the interpolation problem for this configuration.

## Contribution

It provides an explicit minimal bigraded free resolution and Hilbert function for three fat points supported on an ACI in , addressing a specific interpolation problem.

## Key findings

- Explicit minimal bigraded free resolution derived
- Bigraded Hilbert function computed for the configuration
- Solved the interpolation problem for three fat points supported on an ACI

## Abstract

This is an appendix to the recent paper of Favacchio and Guardo. In these notes we describe explicitly a minimal bigraded free resolution and the bigraded Hilbert function of a set of 3 fat points whose support is an almost complete intersection (ACI) in $\mathbb{P}^1\times\mathbb{P}^1.$ This solve the interpolation problem for three points with an ACI support.