Classical deformations of noncompact surfaces and their moduli of instantons
@article{Barmeier2019ClassicalDO, title={Classical deformations of noncompact surfaces and their moduli of instantons}, author={Severin Barmeier and Elizabeth Gasparim}, journal={Journal of Pure and Applied Algebra}, year={2019} }
6 Citations
Deformations of categories of coherent sheaves via quivers with relations
- Mathematics
- 2021
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme X via the deformation theory of path…
20 Open questions about deformations of compactifiable manifolds
- Mathematics
- 2020
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods.
In this note, we recall some concepts of the…
Infinite dimensional families of Calabi–Yau threefolds and moduli of vector bundles
- MathematicsJournal of Pure and Applied Algebra
- 2019
Deformations of path algebras of quivers with relations
- Mathematics
- 2020
Let $A = \Bbbk Q / I$ be the path algebra of any finite quiver $Q$ modulo any finitely generated ideal of relations $I$. We develop a method to give a concrete description of the deformation theory…
A Lie theoretical construction of a Landau–Ginzburg model without projective mirrors
- Mathematicsmanuscripta mathematica
- 2018
We describe the Fukaya–Seidel category of a Landau–Ginzburg model $$\mathrm {LG}(2)$$LG(2) for the semisimple adjoint orbit of $$\mathfrak {sl}(2, {\mathbb {C}})$$sl(2,C). We prove that this category…
Deformation-obstruction theory for diagrams of algebras and applications to geometry
- Mathematics
- 2018
Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the…
References
SHOWING 1-10 OF 39 REFERENCES
Vector Bundles Near Negative Curves: Moduli and Local Euler Characteristic
- Mathematics
- 2009
We study moduli of vector bundles on a two-dimensional neighbourhood Z k of an irreducible curve ℓ ≅ ℙ1 with ℓ2 = −k and give an explicit construction of their moduli stacks. For the case of…
On the deformations of certain moduli spaces of vector bundles
- Mathematics
- 1993
Introduction. Let X be a smooth projective curve of genus g > 2 and Md(n, L) the moduli space of semi-stable bundles E of rank n and degree d, with det(E) z L. When (n, d) = 1 the variety Md(n, L) is…
On Deformations of Pairs (Manifold, Coherent Sheaf)
- MathematicsCanadian Journal of Mathematics
- 2019
Abstract We analyse infinitesimal deformations of pairs $(X,{\mathcal{F}})$ with ${\mathcal{F}}$ a coherent sheaf on a smooth projective variety $X$ over an algebraically closed field of…
The Nekrasov Conjecture for Toric Surfaces
- Mathematics
- 2009
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 $${\mathbb{R}^4}$$, the…
Local holomorphic Euler characteristic and instanton decay
- Mathematics
- 2007
We study the local holomorphic Euler characteristic $\chi(x,\mathcal{F})$ of sheaves near a surface singularity obtained from contracting a line $\ell$ inside a smooth surface $Z$. We prove…
Rank Two Bundles on the Blow-up ofC2☆
- Mathematics
- 1998
In this paper we study holomorphic rank two vector bundles on the blow-up ofC2with vanishing Chern class. The restriction of such a bundle over the exceptional divisor splits as O(j) ⊕ O(−j) for some…
Vector Bundles on a Neighborhood of an Exceptional Curve and Elementary Transformations
- Mathematics
- 2001
Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$…
Holomorphic bundles on O(− k) are algebraic
- Mathematics
- 1996
We show that holomorphic bundles on O(−k) for k>0 are algebraic. We also show that holomorphic bundles on O(−1) are trivial outside the zero section. A corollary is that bundles on the blow-up of a…
A Lie theoretical construction of a Landau–Ginzburg model without projective mirrors
- Mathematicsmanuscripta mathematica
- 2018
We describe the Fukaya–Seidel category of a Landau–Ginzburg model $$\mathrm {LG}(2)$$LG(2) for the semisimple adjoint orbit of $$\mathfrak {sl}(2, {\mathbb {C}})$$sl(2,C). We prove that this category…