Algebra and Geometry Seminar

A projective variety X is called Calabi-Yau if its canonical divisor is Q-linearly equivalent to zero. The smallest positive integer m with mK_X​ linearly equivalent to zero is called the index of X. Using ideas from mirror symmetry, we construct Calabi-Yau varieties with index growing doubly exponentially with dimension. We conjecture they are the largest index in each dimension based on evidence in low dimensions. We also give Calabi-Yau varieties with large orbifold Betti numbers or small minimal log discrepancy. Joint work with Louis Esser and Burt Totaro.