Details:
Title  Computing differential equations for integrals associated to smooth Fano polytope.  Author(s)  Hiromasa Nakayama, Nobuki Takayama  Type  Article in Journal  Abstract  We give an approximation algorithm of computing holonomic systems of linear differential equations for definite integrals of rational functions with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping condition. We apply the approximation method to find differential equations for integrals associated to smooth Fano polytopes. These are interesting in the study of K3 surfaces and the toric mirror symmetry. In this class of integrals, we can apply Stienstra’s rank formula to our algorithm, which gives a stopping condition of the approximation algorithm.  Keywords  Gröbner Basis, Dmodules, Integration algorithm, Period map, CalabiYau variety  ISSN  09167005; 1868937X/e 
URL 
http://link.springer.com/article/10.1007%2Fs1316001301055 
Language  English  Journal  Japan J. Ind. Appl. Math.  Volume  30  Number  2  Pages  307319  Publisher  Springer Japan, Tokyo  Year  2013  Edition  0  Translation 
No  Refereed 
No 
