Conjectures and Computations about Veronese Syzygies

ABSTRACT

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. These conjectures are motivated by experimental data that we derived from a high-speed high-throughput computation of multigraded Betti numbers based on numerical linear algebra.

Keywords:

•  

2000 AMS SUBJECT CLASSIFICATION:

•  

Notes

1 While a few multigraded entries for d = 6 and b = 4, 5 are missing, we also produced some data for d = 7, 8. The computations related to this work will continue: our available hardware was recently upgraded, and we reimplemented one of our core algorithms, with the hope of addressing remaining gaps and generating more data for d > 6.

2 Interestingly, earlier computations where we used a QR-decomposition algorithm seem to have produced minor numerical errors in a small number of multigraded Betti numbers for d = 5.

Additional information

Funding

JB received support from the NSF GRFP under grant DGE-1256259, and from the Graduate School and the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin-Madison with funding from the Wisconsin Alumni Research Foundation. DE received support from NSF grant DMS-1601619. JY received support from NSF grant DMS-1502553.