On logarithmic solutions of Ahypergeometric systems
Abstract
For an $A$hypergeometric system with parameter $\beta$, a vector $v$ with minimal negative support satisfying $Av = \beta$ gives rise to a logarithmfree series solution. We find conditions on $v$ analogous to `minimal negative support' that guarantee the existence of logarithmic solutions of the system and we give explicit formulas for those solutions. Although we do not study in general the question of when these logarithmic solutions lie in a Nilsson ring, we do examine the $A$hypergeometric systems corresponding to the PicardFuchs equations of certain families of complete intersections and we state a conjecture regarding the integrality of the associated mirror maps.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5173
 Bibcode:
 2014arXiv1402.5173A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 23 pages