Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 039, 37 pages      arXiv:1707.08728      https://doi.org/10.3842/SIGMA.2018.039
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds

Shinobu Hosono and Hiromichi Takagi
Department of Mathematics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171-8588, Japan

Received September 11, 2017, in final form April 23, 2018; Published online May 02, 2018

Abstract
We study mirror symmetry of complete intersection Calabi-Yau manifolds which have birational automorphisms of infinite order. We observe that movable cones in birational geometry are transformed, under mirror symmetry, to the monodromy nilpotent cones which are naturally glued together.

Key words: Calabi-Yau manifolds; mirror symmetry; birational geometry; Hodge theory.

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