15:30 - 17:00, November 22, 2024 (Friday) Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
Automorphisms with Zariski dense orbits of Calabi-Yau threefolds with birational $c_2$-contraction Keiji Oguiso (University of Tokyo)
Abstract
We work over or . In algebraic geometry and algebraic dynamics, for given a projective variety and a birational selfmap , it is natural to study (i) dynamical degrees of (ii) the existence of Zariski dense orbit of , (iii) non-existence of equivariant non-trivial rational fibration with respect to (primitivity of ) and, (iv) non-existence of invariant rational functions with respect to .
After explaining some back ground, motivation of the problem from algebraic geometry, algebraic and arithmetic dynamics, I would like to consider these four properies of an automorphism of a Calabi-Yau threefold , with some hidden roles of the second Chern class in this study.
First, I would like to deduce that, under two notorious but natural conjectures, there are exactly two Calabi-Yau threefolds with an automorphism of Zariski dense orbit.
Then, I would like to show the (unconditional) relations among properties (i) -(iv) on automorphisms of these two Calabi-Yau threefolds, with an explicit description of their automorphism groups, some idea of proof and explicit examples.
