Ulrich ranks on the Veronese fivefold X^5_2: existence for ranks 8k with odd k < 15

Determine whether the Veronese fivefold X^5_2 (the 2-uple Veronese embedding of P^5) admits Ulrich bundles of rank 8k for odd integers k < 15.

Background

For n=5 and d=2, the paper observes via arithmetic constraints that any Ulrich bundle must have rank divisible by 8. Using representation-theoretic constructions (an SL6-bundle associated to the irreducible representation of highest weight ϖ2+ϖ3), they exhibit an Ulrich bundle of rank 16 on X^5_2.

However, the existence of Ulrich bundles for many other admissible ranks remains unknown. In particular, the authors highlight the open cases for ranks 8k with odd k < 15 (i.e., 8, 24, 40, 56, 72, 88, 104), where current methods do not decide existence.