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Commutative Algebra Seminar in Beijing
A Betti stratification of apolar ideals to quaternary quartics, II
A Betti stratification of apolar ideals to quaternary quartics, II
Organizers
Ming Fang
, Manolis Tsakiris
,
Bei Hui Yuan
Speaker
Time
Saturday, March 16, 2024 9:30 AM - 11:30 AM
Venue
AMSS-N208
Abstract
In the second of two lectures, I am going to draw people's attention to the ``geometry of syzygies". We begin with a research problem from geometry: Finding all Gorenstein Calabi-Yau varieties. In dimension 3 cases, their coordinate rings have regularity 4. There are 16 Betti diagrams for such graded Gorenstein algebras with projective dimension 4. By apolarity, they correspond to degree 4 forms in 4 variables, i.e. quaternary quartics. Note that the Betti diagram encodes how the algebraic set is embedded in the ambient space. In fact, each of the 16 Betti diagrams corresponds to the geometric description of the apolar set, which is a set of points in a projective space. With this description, we find a stratification of the parameter space of quaternary quartics.
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.