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.
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.