Related papers: Rational Curves on Moduli Spaces of Vector Bundles

The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also…

We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our…

Let $E$ be a vector bundle of rank $r\geq 2$ on a smooth projective curve $C$ of genus $g \geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\le k\le r-1$ we define $${\se}_k(E):=k\deg…

A lot is known about the moduli space of parabolic bundles over curves of genus $g\geq 2$, but the lower genus cases are notably different. The goal of this article is to study the geometry of the moduli space of semistable parabolic…

Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use families of curves on…

We determine all of lines in the moduli space $M$ of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

Let C be a smooth projective curve of genus at least 2 over a field k. Given a line bundle L on C, we consider the moduli stack of rank 2n vector bundles E on C endowed with a nowhere degenerate symplectic form $b: E \otimes E \to L$ up to…

Let SU(r,d) be the moduli space of rank r, degree d vector bundles over a smooth projective curve of genus $g\ge 2$. If (r,d)=1 and d divides r+1, then SU is rational. Furthermore, if $0<\delta < r$ and all prime divisors of $\delta$ divide…

Resume Soit SU_C(r) l'espace des modules des fibr\'es vectoriels semi-stables de d\'eterminant trivial sur une courbe lisse $C$ de genre $g \geq 2$ sur $\mathbb{C}$. On \'etudie dans cet article, un exemple de fibr\'e introduit par Raynaud…

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define $\Hi^{\prec\Delta}_{S/k}$, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open…

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…

As a continuation of the work of Freiermuth and Trautmann, we study the geometry of the moduli space of stable sheaves on $\mathbb{P}^3$ with Hilbert polynomial $4m+1$. The moduli space has three irreducible components whose generic…

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli…

We prove that any vector bundle computing the rank-two Clifford index of a smooth projective algebraic curve is linearly semistable. We also identify conditions under which such bundles become linearly stable, thereby addressing a question…

Sheaves on non-reduced curves can appear in moduli space of 1-dimensional semistable sheaves over a surface, and moduli space of Higgs bundles as well. We estimate the dimension of the stack $\mathbf{M}_{X}(nC,\chi)$ of pure sheaves…

We determine the splitting (isomorphism) type of the normal bundle of a generic genus-0 curve with 1 or 2 components in any projective space, as well as the (sometimes nontrivial) way the bundle deforms locally with a general deformation of…

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to different ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying…