Homological methods for hypergeometric families

  title={Homological methods for hypergeometric families},
  author={Laura Felicia Matusevich and Ezra Miller and Uli Walther},
  journal={Journal of the American Mathematical Society},
We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we investigate rank-jump behavior for hypergeometric systems H_A(\beta) arising from a d x n integer matrix A and a parameter \beta \in \CC^d. To do so we introduce an Euler-Koszul functor for hypergeometric families over \CC^d, whose homology generalizes the notion of a hypergeometric system, and we prove… 
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