Big Vector Bundles on Surfaces and Fourfolds

Bini, Gilberto; Flamini, Flaminio

doi:10.1007/s00009-019-1463-2

Cited by 3 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [7], we introduced cohomological criteria on algebraic surfaces and fourfolds in order to verify the numerical characterization mentioned before. What's more, we found out examples of big vector bundles (split and unsplit) on Hirzebruch surfaces and investigated the bigness of some families of Mukai-Lazarsfeld bundles on regular fourfolds.…”

Section: Introductionmentioning

confidence: 99%

Some families of big and stable bundles on $K3$ surfaces and on their Hilbert schemes of points

Bini¹,

Boissière²,

Flamini³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Here we investigate meaningful families of vector bundles on a very general polarized K3 surface (X, H) and on the corresponding Hyper-Kähler variety given by the Hilbert scheme of points X [k] := Hilb k (X), for any integer k 2. In particular, we prove results concerning bigness and stability of such bundles. First, we give conditions on integers n such that the twist of the tangent bundle of X by the line bundle nH turns out to be big and stable on X; we then prove a similar result for a natural twist of the tangent bundle of X [k] . Next, by a careful analysis on Segre classes, we prove bigness and stability results for tautological bundles on X [k] arising either from line bundles or from Mukai-Lazarsfeld bundles, as well as from Ulrich bundles on X.

show abstract

Section: Introductionmentioning

confidence: 99%