Newton polytopes and algebraic hypergeometric series
| Autor: | Adolphson, Alan, Sperber, Steven |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $X$ be the family of hypersurfaces in the odd-dimensional torus ${\mathbb T}^{2n+1}$ defined by a Laurent polynomial $f$ with fixed exponents and variable coefficients. We show that if $n\Delta$, the dilation of the Newton polytope $\Delta$ of $f$ by the factor $n$, contains no interior lattice points, then the Picard-Fuchs equation of $W_{2n}H^{2n}_{\rm DR}(X)$ has a full set of algebraic solutions (where $W_\bullet$ denotes the weight filtration on de Rham cohomology). We also describe a procedure for finding solutions of these Picard-Fuchs equations. Comment: With an appendix by Nicholas Katz |
| Databáze: | arXiv |
| Externí odkaz: |
|