{"paper":{"title":"The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.AG","authors_text":"Victor Batyrev","submitted_at":"2017-07-09T17:02:35Z","abstract_excerpt":"We show that minimal models of nondegenerated hypersufaces defined by Laurent polynomials with a $d$-dimensional Newton polytope $\\Delta$ are Calabi-Yau varieties $X$ if and only if the Fine interior of $\\Delta$ consists of a single lattice point. We give a combinatorial formula for computing the stringy Euler number of $X$. This formula allows to test mirror symmetry in cases when $\\Delta$ is not a reflexive polytope. In particular we apply this formula to pairs of lattice polytopes $(\\Delta, \\Delta^{\\vee})$ that appear in the Mavlyutov's generalization of the polar duality for reflexive poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02602","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}