{ "id": "1606.04210", "version": "v1", "published": "2016-06-14T06:28:31.000Z", "updated": "2016-06-14T06:28:31.000Z", "title": "The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians", "authors": [ "Atsushi Ito", "Makoto Miura", "Shinnosuke Okawa", "Kazushi Ueda" ], "comment": "5 pages", "categories": [ "math.AG" ], "abstract": "Motivated by [Bor] and [Mar], we show the equality $\\left([X] - [Y]\\right) \\cdot [\\mathbb{A}^1] = 0$ in the Grothendieck ring of varieties, where $(X, Y)$ is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type $G_2$.", "revisions": [ { "version": "v1", "updated": "2016-06-14T06:28:31.000Z" } ], "analyses": { "keywords": [ "affine line", "zero divisor", "grothendieck ring", "grassmannians" ], "note": { "typesetting": "TeX", "pages": 5, "language": "en", "license": "arXiv", "status": "editable" } } }