Moduli of bundles on the blown-up plane (original) (raw)

Numerical invariants for bundles on blow-ups

1999

We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces M_j of bundles on the blown-up plane splitting over the exceptional divisor as O(j)+O(-j). We use the numerical invariants to give a topological decomposition of M_j.

Holomorphic bundles on the blown-up plane and the bar construction

Algebraic & Geometric Topology, 2020

Let M 0 = ' BU (k), M 1 = ' (BU (k) × BU (k)). We construct a map from Bar`M 0 , M n 0 , M n 1´t o the rank-stable moduli space of holomorphic bundles on the blowup of P 2 at n points, framed on a rational curve. We show that this map is a homotopy equivalence in the degree 1 and 2 components and in the limit when k → ∞.

Vector Bundles Near Negative Curves: Moduli and Local Euler Characteristic

Communications in Algebra, 2009

We study moduli of vector bundles on a two-dimensional neighbourhood Z k of an irreducible curve ℓ ∼ = P 1 with ℓ 2 = −k and give an explicit construction of their moduli stacks. For the case of instanton bundles, we stratify the stacks and construct moduli spaces. We give sharp bounds for the local holomorphic Euler characteristic of bundles on Z k and prove existence of families of bundles with prescribed numerical invariants. Our numerical calculations are performed using a Macaulay 2 algorithm, which is available for download at http://www.maths.ed.ac.uk/ ∼ s0571100/Instanton/.

Moduli Spaces of Sheaves on General Blow-ups of mathbbP2\mathbb{P}^2mathbbP2

Cornell University - arXiv, 2022

Let X be the blow-up of P 2 along m general points, and A = H − εiEi be a generic polarization with 0 < εi ≪ 1. We classify the Chern characters which satisfy the weak Brill-Noether property, i.e. a general sheaf in MA(v), the moduli space of slope stable sheaves with Chern character v, has at most one non-zero cohomology. We further give a necessary and sufficient condition for the existence of stable sheaves. Our strategy is to specialize to the case when the m points are collinear. 2 Preliminaries Convention. By a surface, we mean a connected smooth projective algebraic surface over C. All sheaves are coherent unless specified. For a surface X and coherent sheaves E and F , we write h i (X, E) = dim H i (X, E), hom(E, F) = dim Hom(E, F), and ext i (E, F) = dim Ext i (E, F). 2.1 Chern characters and Riemann-Roch on surfaces Let E be a torsion-free sheaf on a polarized surface (X, A). Let K(X) Q be the Grothendieck group of X with Q-coefficients. The Chern character ch(E) = (ch 0 (E), ch 1 (E), ch 2 (E)

Holomorphic Rank Two Vector Bundles on Blow-ups

1996

In this paper we study holomorphic rank two vector bundles on the blow up of $ {\bf C}^2$ at the origin. A classical theorem of Birchoff and Grothendieck says that any holomorphic vector bundle on the projective plane bfP1{\bf P}^1bfP1 splits into a sum of line bundles. If EEE is a holomorphic vector bundle over the blow up of $

On the new compactification of moduli of vector bundles on a surface. II

Sbornik: Mathematics, 2009

A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial, on the smooth projective polarized surface (S, L), is constructed. We work over the field k =k of characteristic zero. Families of locally free sheaves on the surface S are completed with locally free sheaves on schemes which are modifications of S. Gieseker-Maruyama moduli space has a birational morphism onto the new moduli space. We propose the functor for families of pairs "polarized scheme-vector bundle" with moduli space of such type.