Two types of actions are possible depending in the objective of the trademark holder. In this respect, the possibility to claim compensation and the reimbursement of the attorney fees may be a crucial issue in the decision-making process for a judicial action in the US.
If this objective is pursued, the choice of an action in personam may constitute an appealing choice. It is ground on the capacity of the parties to activate the jurisdiction of a US Federal Court (the registrant is domiciled in the US, the trademark owner has right protected in the US) and authorizes the claimant to claim compensation and reimbursement of attorney fees.
Since this action cannot cover all situations, it should be noted that an action in rem in other words directed against the domain name themselves may be considered for the registrant that cannot fit in the first category.
Dreyfus is at your disposal for any advice you might need.