Syzygies of ${\mathbb{P}}^1\times {\mathbb{P}}^1$: data and conjectures

Abstract

We provide a number of new conjectures and questions concerning the syzygies of ${\mathbb{P}}^1\times {\mathbb{P}}^1$. The conjectures are based on computing the graded Betti tables and related data for large number of different embeddings of ${\mathbb{P}}^1\times {\mathbb{P}}^1$. These computations utilize linear algebra over finite fields and high-performance computing.

References in corpus (9)

• Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture
• Asymptotic syzygies of algebraic varieties
• Tensor complexes: Multilinear free resolutions constructed from higher tensors
• Categorified duality in Boij-Söderberg Theory and invariants of free complexes
• The linear space of Betti diagrams of multigraded artinian modules
• Shapes of free resolutions over a local ring
• Asymptotic Syzygies in the Setting of Semi-Ample Growth
• Rational combinations of Betti diagrams of complete intersections
• Recursive strategy for decomposing Betti tables of complete intersections