Jets of graphs

The notion of jets comes from differential geometry and it captures higher order differential approximations of a space, generalizing the concept of tangent bundle. Jets have been adopted in algebraic geometry as a tool to study singularities. Although the equations of jets can be easily written down, many questions about jet spaces remain open, particularly their decomposition into irreducible components. Our work focuses on spaces defined by squarefree monomial equations, which allows us to employ techniques from algebra and combinatorics. We define jets of graphs and use properties of their covers to address decompositions of the corresponding spaces.
 

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