Courses / ActivitiesIntroduction to the interrelation between affine manifolds and toric degeneration of Calabi-Yau pairs (after Gross and Siebert) 3
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In recent years, Gross and Siebert have proposed a program to study Mirror symmetry by studying the log structure on degeneration of Calabi-Yau manifolds. In their foundational work [1], it was shown that to each degeneration of certain types one can associate an affine manifold (with singularities) and conversely, given any such affine manifold, one can create a "log Calabi-Yau space" playing a potential role of the central fiber of some sort of degeneration. In [2], they indicate how to construct a formal degeneration with this log Calabi-Yau space its central fiber. Under some conditions, basic results in algebraic geometry then imply the existence of a genuine degeneration. We will give a brief survey of [2]. Reference: Gross and Siebert's articles-- [1] Mirror symmetry via logarithmic degeneration data I, JDG 72 (2006) [2] From real affine geometry to complex geometry, Annals of Mathematics 174 (2011).
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Chen-Yu Chi
2012-01-18
13:00:00 - 15:00:00
R101 , Astronomy and Mathematics Building
In recent years, Gross and Siebert have proposed a program to study Mirror symmetry by studying the log structure on degeneration of Calabi-Yau manifolds. In their foundational work [1], it was shown that to each degeneration of certain types one can associate an affine manifold (with singularities) and conversely, given any such affine manifold, one can create a "log Calabi-Yau space" playing a potential role of the central fiber of some sort of degeneration. In [2], they indicate how to construct a formal degeneration with this log Calabi-Yau space its central fiber. Under some conditions, basic results in algebraic geometry then imply the existence of a genuine degeneration. We will give a brief survey of [2]. Reference: Gross and Siebert's articles-- [1] Mirror symmetry via logarithmic degeneration data I, JDG 72 (2006) [2] From real affine geometry to complex geometry, Annals of Mathematics 174 (2011).