Abstract
Birational maps give the main research tool for the theory of Fano varieties, as we know from the fundamental works of V.A. Iskovskikh and his school. Nowadays one can exploit them in the new approach of D. Auroux to Mirror Symmetry of Fano varieties, which is based on a certain generalization of the notion of special Lagrangian fibration suitable for Fano varieties. We present a very simple example of how a special Lagrangian fibration can be transferred by a birational map.
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References
D. Auroux, “Mirror Symmetry and T-Duality in the Complement of an Anticanonical Divisor,” J. Gökova Geom. Topol. 1, 51–91 (2007); arXiv: 0706.3207.
P. Griffiths and J. Harris, Principles of Algebraic Geometry (Wiley, New York, 1978).
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 209–211.
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Tyurin, N.A. Birational maps and special Lagrangian fibrations. Proc. Steklov Inst. Math. 264, 201–203 (2009). https://doi.org/10.1134/S0081543809010209
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DOI: https://doi.org/10.1134/S0081543809010209