In this paper we investigate stable vector bundles on the complex projective plane P by means of their minimal free resolution. The fundamental background for this study is the work of Bohnhorst and Spindler [BS92] and their idea to use admissible pairs to characterize the stability of rank-n vector bundles on P and to give a stratification of the relative moduli space in constructible subsets....

1 The Cotangent Complex: General Theory 4 1.1 Stable Envelopes and Tangent Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Relative Adjunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 The Tangent Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 The Relative Cotangent Complex...

Introduction 1 1. Representations of the fundamental group 3 2. Abelian groups and rank one Higgs bundles 5 3. Stable vector bundles and Higgs bundles 6 4. Hyperbolic geometry: G = PSL(2,R) 8 5. Moduli of hyperbolic structures and representations 13 6. Rank two Higgs bundles 19 7. Split R-forms and Hitchin’s Teichmüller component 21 8. Hermitian symmetric spaces: Maximal representations 24 Refe...

Contents Introduction 3 1. Foundations 13 1.1. A survey about the theory of tight closure 13 1.2. Solid closure and forcing algebras 23 1.3. Cohomological dimension 25 1.4. Vector bundles, locally free sheaves and projective bundles 28 2. Geometric interpretation of tight closure via bundles 30 2.1. Relation bundles 30 2.2. Affine-linear bundles arising from forcing algebras 32 2.3. Cohomology ...

In this paper, we contribute to the construction of families arithmetically Cohen–Macaulay (aCM) indecomposable vector bundles on a wide range polarized surfaces [Formula: see text] for an ample line bundle. many cases, show that every positive integer there exists family aCM rank text], depending roughly parameters, and in particular they are wild representation type. We also introduce general...