A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES

Note: Vector Bundles on Curves

The information above on email or mailbox is obsolete. Thanks to Ulrich Görtz for providing me with a copy of the original postscript file. Lectures by Gerd Faltings held in Bonn 1995 Notes by Michael Stoll Comments, remarks, questions etc. inserted by me are set in slanted. Contributions by other people are set in sans serif and marked by their initials: ck] Christian Kaiser Since these notes ...

A Note on Moduli of Vector Bundles on Rational Surfaces

Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

A Note on Exponentially Nash G Manifolds and Vector Bundles

Notes on Vector Bundles

−→ V, (v1, v2) −→ v1+v2, are smooth. Note that we can add v1, v2∈V only if they lie in the same fiber over M , i.e. π(v1)=π(v2) ⇐⇒ (v1, v2) ∈ V ×M V. The space V ×M V is a smooth submanifold of V ×V , as follows immediately from the Implicit Function Theorem or can be seen directly. The local triviality condition means that for every point m∈M there exist a neighborhood U of m in M and a diffeo...

Vector bundles on Orbispaces

Orbispaces are spaces with extra structure. The main examples come from compact Lie group actionsX G and are denoted [X/G], their underlying space being X/G. By definition, every orbispace is locally of the form [X/G], but the group G might vary. To be more precise, an orbispace is a topological stack which is locally equivalent to [X/G] for G a Lie group and X a G-CW-complex [2] [4] [5]. Howev...