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Holomorphic fibrations on Calabi-Yau manifolds and collapsing

Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016

March 21, 2016 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Valentino Tosatti (Northwestern University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • mathematical physics

  • complex differential geometry

  • Kahler metric

  • mirror symmetry

  • Calabi-Yau manifold

  • Ricci curvature

  • Ricci flatness

  • algebraic geometry and GAGA

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Consider a compact Calabi-Yau manifolds with a holomorphic fibration onto a lower-dimensional base. Pulling back a Kahler class from the base, we obtain a class on the boundary of the Kahler cone, which is a limit of Kahler classes. These classes contain Ricci-flat metrics, which in the limit collapse to a twisted Kahler-Einstein metric on the base (away from the singular fibers). Furthermore if we rescale so that the fibers have fixed size, then away from the singular fibers the limit is a cylinder over a Ricci-flat fiber. This is based on joint work with Weinkove and Yang, with Hein and with Zhang, and is directly related to the topic of the talk by Mark Gross

Supplements No Notes/Supplements Uploaded
Video/Audio Files

14458

H.264 Video 14458.mp4 357 MB video/mp4 rtsp://videos.msri.org/data/000/025/568/original/14458.mp4 Download
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