On the construction of Weakly Ulrich bundles

Abstract

I provide a construction of intrinsic weakly Ulrich bundles of large rank on any smooth complete surface in ${\mathbf{P}}^3$ over fields of characteristic $p>0$ and also for some classes of surfaces of general type in ${\mathbf{P}}^n$. I also construct intrinsic weakly Ulrich bundles on any Frobenius split variety of dimension at most three. The bundles constructed here are in fact ACM and weakly Ulrich bundles and so I call them almost Ulrich bundles. Frobenius split varieties in dimension three include as special cases: (1) smooth hypersurfaces in ${\mathbf{P}}^4$ of degree at most four, (2) Frobenius split, smooth quintics in ${\mathbf{P}}^4$ (3) Frobenius split Calabi-Yau varieties of dimension at most three (4) Frobenius split (i.e ordinary) abelian varieties of dimension at most three.

7 pages; To appear in Advances in Math

References in corpus (2)

• A remark on Ulrich and ACM bundles
• On determinantal equations for curves and Frobenius split hypersurfaces

Cited by in corpus (1)

• Corrigendum: On the construction of Weakly Ulrich bundles