On a sufficient condition for a Fano manifold to be covered by rational N-folds |
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| Institution: | 1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic;2. Department of Mathematics, Harvard University, Cambridge, MA, USA;1. Department of Mathematics, University of Puerto Rico, Río Piedras, 17 Ave Universidad Ste 1701, S.J., PR 00925-2537, United States of America;2. Gauss Research Foundation, PO Box 21613, S.J., PR 00931, United States of America;3. Department of Computer Science, University of Puerto Rico, Río Piedras, 17 Ave Universidad Ste 1701, S.J., PR 00925-2537, United States of America;1. Institut de recherche en mathématique et physique, Université catholique de Louvain, Chemin du Cyclotron 2, B 1348 Louvain-la-Neuve, Belgique;2. Dipartimento di matematica, Università degli studi di Milano, Via C. Saldini 50, 20133 Milano, Italy;3. Dipartimento di matematica e informatica, Università degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy;4. Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, K1N 6N5, Canada;1. Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada;2. Department of Mathematics, University of California, Riverside, Riverside, CA 92521, United States |
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| Abstract: | In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern characters, then it can be covered by rational N-folds. We prove this conjecture by using purely combinatorial properties of Bernoulli numbers. |
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| Keywords: | Fano manifolds Rational curves Covered by rational manifolds Bernoulli numbers |
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