Calabi-Yau 3-folds in projective spaces and Gorenstein rings
Organizers
Speaker
Time
Thursday, September 21, 2023 3:30 PM - 5:00 PM
Venue
YMSC-Jingzhai-304
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The defining ideal $I_X$ of a projectively normal Calabi-Yau 3-fold $X$ is arithmetically Gorenstein, of Castelnuovo-Mumford regularity 4. Such ideals have been intensively studied when $I_X$ is a complete intersection, as well as in the case where $X$ has codimension 3. In the latter case, the Buchsbaum-Eisenbud theorem shows that $I_X$ is given by the Pfaffians of a skew-symmetric matrix. A number of recent papers study the situation when $I_X$ has codimension 4. We prove there are 16 possible Betti tables for an arithmetically Gorenstein ideal with codimension 4 and regularity 4, and that 8 of these arise for prime nondegenerate 3-folds. A main feature of our approach is the use of inverse systems to identify possible Betti tables for $X$. This is a joint work with H. Schenck and M. Stillman.
Speaker Intro
Beihui Yuan gained her Ph.D. degree from Cornell University in 2021. She has joined BIMSA in 2023. Her current research interests include application of commutative algebra in pure and applied mathematics problems.