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In this paper, we prove that the normal bundle of a general Brill-Noether space curve of degree $d$ and genus $g geq 2$ is stable if and only if $(d,g) otin { (5,2), (6,4) }$. When $gleq1$ and the characteristic of the ground field is zero, it is classical that the normal bundle is strictly semistable. We show that this fails in characteristic $2$ for all rational curves of even degree.
We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a choice of stab
We show that given integers $N$, $d$ and $n$ such that ${Nge2}$, ${(N,d,n) e(2,2,5)}$, and ${N+1le nletbinom{d+N}{N}}$, there is a family of $n$ monomials in $K[X_0,ldots,X_N]$ of degree $d$ such that their syzygy bundle is stable. Case ${Nge3}$ was
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Grassmannian. It has all the properties asked for by Teixidor.
It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle $E_{d_1,...,d_n}$ on $mathbb{P}^N$ defined as the kernel of a general epimorphism [phi:mathcal{O}(-d_1)oplus...oplusmathcal{O}(-d_n) tomathcal{O}] is (semi)stab
A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus $gge 1$ is itself a ruled surface over a curve of genus $g$. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case $gge 2$.