37 research outputs found
Three Applications of Instanton Numbers
We use instanton numbers to: (i) stratify moduli of vector bundles, (ii)
calculate relative homology of moduli spaces and (iii) distinguish curve
singularities.Comment: To appear in Communications in Mathematical Physic
Moduli Stacks of Bundles on Local Surfaces
We give an explicit groupoid presentation of certain stacks of vector bundles
on formal neighborhoods of rational curves inside algebraic surfaces. The
presentation involves a M\"obius type action of an automorphism group on a
space of extensions.Comment: submitted upon invitation to the 2011 Mirror Symmetry and Tropical
Geometry Conference (Cetraro, Italy) volume of the Springer Lecture Notes in
Mathematic
Local moduli of holomorphic bundles
We study moduli of holomorphic vector bundles on non-compact varieties. We
discuss filtrability and algebraicity of bundles and calculate dimensions of
local moduli. As particularly interesting examples, we describe numerical
invariants of bundles on some local Calabi-Yau threefolds.Comment: 18 pages. Revision history: v1: As submitted for publication. v2:
minor corrections, as publishe
Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces
We construct a compactification of the Uhlenbeck-Donaldson type
for the moduli space of slope stable framed bundles. This is a kind of a moduli
space of slope semistable framed sheaves. We show that there exists a
projective morphism , where is
the moduli space of S-equivalence classes of Gieseker-semistable framed
sheaves. The space has a natural set-theoretic stratification
which allows one, via a Hitchin-Kobayashi correspondence, to compare it with
the moduli spaces of framed ideal instantons.Comment: 18 pages. v2: a few very minor changes. v3: 27 pages. Several proofs
have been considerably expanded, and more explanations have been added. v4:
28 pages. A few minor changes. Final version accepted for publication in
Math.
The Nekrasov Conjecture for Toric Surfaces
The Nekrasov conjecture predicts a relation between the partition function
for N=2 supersymmetric Yang-Mills theory and the Seiberg-Witten prepotential.
For instantons on R^4, the conjecture was proved, independently and using
different methods, by Nekrasov-Okounkov, Nakajima-Yoshioka, and
Braverman-Etingof. We prove a generalized version of the conjecture for
instantons on noncompact toric surfaces.Comment: 38 pages; typos corrected, references added, minor changes (e.g.
minor change of convention in Definition 5.13, 5.19, 6.5