On logarithmic solutions of A-hypergeometric systems
On logarithmic solutions of A-hypergeometric systems
复制标题
A-超几何系统的对数解
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
S. Sperber
中科院分区：
文献类型：
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作者：
A. Adolphson;S. Sperber
对于一个带参数$\beta$的$A$-超几何系统，一个具有最小负支集满足$Av = \beta$的向量$v$产生一个无偏级数解.我们发现条件$v$类似于“最小负支持”，保证系统的对数解的存在，我们给这些解决方案的明确公式。虽然我们不研究一般的问题时，这些对数的解决方案在于一个尼尔森环，我们检查$A$-超几何系统对应的皮卡德-富克斯方程的某些家庭的完整的交叉点，我们国家的一个猜想有关的完整性相关的镜像地图。
For an $A$-hypergeometric system with parameter $\beta$, a vector $v$ with minimal negative support satisfying $Av = \beta$ gives rise to a logarithm-free 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 Picard-Fuchs equations of certain families of complete intersections and we state a conjecture regarding the integrality of the associated mirror maps.