The geometry of Ulrich bundles on del Pezzo surfaces

Details The geometry of Ulrich bundles on del Pezzo surfaces The geometry of Ulrich bundles on del Pezzo surfaces

2011-05-12

arxiv.org/abs/1105.2575v3

Mathematics

Algebraic Geometry

23 pages, section added on the case of Arithmetically Gorenstein surfaces and minor revisions

Scientific paper

Given a smooth del Pezzo surface $X_d \subseteq \mathbb{P}^{d}$ of degree $d,$ we show that a smooth irreducible curve $C$ on $X_d$ represents the first Chern class of an Ulrich bundle on $X_d$ if and only if its kernel bundle $M_C$ admits a generalized theta-divisor. This result is applied to produce new examples of complete intersection curves with semistable kernel bundle, and also combined with work of Farkas-Musta\c{t}\v{a}-Popa to relate the existence of Ulrich bundles on $X_d$ to the Minimal Resolution Conjecture for curves lying on $X_d.$ In particular, we show that a smooth irreducible curve $C$ of degree $3r$ lying on a smooth cubic surface $X_3$ represents the first Chern class of an Ulrich bundle on $X_3$ if and only if the Minimal Resolution Conjecture holds for $C.$

Affiliated with

Also associated with

No associations

Rating

The geometry of Ulrich bundles on del Pezzo surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The geometry of Ulrich bundles on del Pezzo surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The geometry of Ulrich bundles on del Pezzo surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26532