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The aim of this paper is to study the associated primes of powers ofsquarefree monomial ideals. Hypergraphs and squarefree monomial ideals arestrongly connected. The cover ideal $J(H)$ of a hypergraph $H$ is theintersection of the primes corresponding to the edges of $H$. We define the$shadow$ of $H$ as a certain set of smaller hypergraphs related to $H$. We thendescribe how the shadows of $H$ preserve information about the associatedprimes of the powers of $J(H)$. Some implications to the persistence propertyare studied.

In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals