We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are t
We show the kernel sheaf associated to a sufficiently positive torsion-free sheaf of rank one is slope stable. Furthermore, we are able to give an explicit bound for "sufficiently positive." This settles a conjecture of Ein–Lazarsfeld–Mustopa. The main technical lemma is a bound on the nu...
Remark 1.8 There is recent work of Snowden–Tsimerman that characterizes those rank 2 Ql sheaves on a curve over a number field that come from a family of elliptic curves [60]. This work was very inspiring for us, but the techniques used there are rather different from those used here....
Letbe a smooth, geometrically connected variety. ForXprojective, we prove a Lefschetz-style theorem for abelian schemes of-type onX, modeled after a theorem of Simpson. Inspired by work of Corlette-Simpson over, we formulate a conjecture that absolutely irreducible rank 2 local systems with infin...
Let A be a del Pezzo order on the projective plane over the field of complex numbers. We prove that every torsion-free A-module of rank one can be deformed into a locally free A-module of rank one.doi:10.1016/j.jalgebra.2017.08.029Norbert Hoffmann...
In particular, if X is a K3 surface which is lattice polarized by the lattice \(M_n = M \oplus \langle -2n \rangle \), then X can be expressed as a resolution of one of the surfaces X(a, b, d). One may ask whether the subvarieties of the (a, b, d) domain corresponding...
We show the kernel sheaf associated to a sufficiently positive torsion-free sheaf of rank one is slope stable. Furthermore, we are able to give an explicit bound for "sufficiently positive." This settles a conjecture of Ein–Lazarsfeld–Mustopa. The main technical lemma is a bound on the ...