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

Juliette Bruce; Daniel Corey; Daniel Erman; Steve Goldstein; Robert P. Laudone; Jay Yang

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

Commutative Algebra 2021-05-03 v1 Algebraic Geometry

Authors: Juliette Bruce , Daniel Corey , Daniel Erman , Steve Goldstein , Robert P. Laudone , Jay Yang

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.

Keywords

syzygies graded betti tables embeddings linear algebra over finite fields high-performance computing projective space product

Cite

@article{arxiv.2104.14598,
  title  = {Syzygies of $\mathbb{P}^{1}\times \mathbb{P}^{1}$: data and conjectures},
  author = {Juliette Bruce and Daniel Corey and Daniel Erman and Steve Goldstein and Robert P. Laudone and Jay Yang},
  journal= {arXiv preprint arXiv:2104.14598},
  year   = {2021}
}

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

Abstract

Keywords

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