A-hypergeometric Systems and Embedded Primes
نویسنده
چکیده
The holonomic rank of an A-hypergeometric system HA(β) is conjectured to be independent of the parameter vector β if and only if the toric ideal IA is Cohen Macaulay. We attack this conjecture by explicitly constructing more than vol (A) many linearly independent hypergeometric functions for parameters β coming from embedded primes of certain initial ideals of IA. As a consequence, we prove the conjecture for generic toric ideals and for toric ideals with a full Gale diagram. For the latter class, rank (HA(β))− vol (A) can be arbitrarily large.
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