Calabi-Yau varieties of large index

Abstract: A projective variety $X$ is called Calabi-Yau if its canonical divisor is $\mathbb{Q}$-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.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Chengxi Wang’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-12-02-cw (and will be deleted after ~3-7 days).

---

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

---