代数幾何学セミナー


2018/2/23(Fri)

16:30--17:30 理学部 b棟 b342/346(代数幾何学小研究集会と兼ねています)

Ryo Kanda

大阪大学 理学研究科

Normal extensions of Artin-Schelter regular algebras and flat families of Calabi-Yau central extensions

abstract: This is a joint work with Alex Chirvasitu and S. Paul Smith. We introduce a new method to construct 4-dimensional Artin-Schelter regular algebras as normal extensions of 3- dimensional ones. When this is applied to a 3-Calabi-Yau algebra, we obtain 4-Calabi-Yau algebras that form a flat family over a projective space. Our method is a rich source of new 4-dimensional regular algebras. On the other hand, some of the 4-dimensional regular algebras discovered by Lu-Palmieri-Wu-Zhang arise as outputs of our construction, and our result gives a new proof of regularity for those algebras.