Algebraic Geometry: “Mirror transitions and the Batyrev-Borisov construction”

Dr. Karl Fredrickson, UCR

Thursday, February 21, 2013
  1:10–2 p.m.

The idea of a "transition" between two nonsingular Calabi-Yau threefolds $X$ and $Y$ involves degenerating $X$ to a singular variety $X_0$, then obtaining $Y$ as a resolution of singularities of $X_0$.  David Morrison conjectured that if $X$ and $Y$ are Calabi-Yau threefolds related by a transition and $X^*$ and $Y^*$ are their mirrors, then $X^*$ and $Y^*$ are also related by a transition, but with the degeneration and resolution switched.  In this talk I will discuss some examples that show how the idea of transitions between Calabi-Yau threefolds is related to Batyrev-Borisov mirror symmetry, which is the standard method for constructing mirrors of Calabi-Yau complete intersections in toric varieties.