Numerically flat Higgs vector bundles

After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.Comment: 11 page

Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces

We construct a compactification $M^{\mu ss}$ 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 $\gamma \colon M^{ss} \to M^{\mu ss}$, where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ 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.

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page

Picard group of hypersurfaces in toric 3-folds

We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.Comment: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final version to appear in Int. J. Math., incorporates many (mainly expository) changes suggested by the refere

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.Comment: 29 pages, one more reference adde

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale \alpha' in the low-energy effective action through the stringy non-perturbative sector.Comment: 22 pages, 1 figur

Fracture toughness of AlSi10Mg alloy produced by direct energy deposition with different crack plane orientations

The fracture and tensile behaviors of the AlSi10Mg alloy processed by Direct Energy Deposition were investigated. Three-point bending fracture toughness and tensile specimens were tested at room temperature along different crack plane orientations and loading directions. Before being machined and tested, the printed samples were subjected to heat treatment at 300 °C for 2 h to relieve the residual stresses. Microstructural and fractographic analyses were performed to investigate the fracture mechanisms and the crack propagation paths for each crack orientation. Significant differences in the fracture toughness were observed among the crack plane orientations. Specimens with cracks oriented in the X-Y direction featured the highest fracture toughness values (JIc = 11.96 kJ/m2), whereas the Z-Y crack orientation (perpendicular to the printing direction) performed the lowest fracture toughness values (JIc = 8.91 kJ/m2). The anisotropy in fracture toughness is mainly related to a preferential crack propagation path along the melt pool boundaries. At melt pool boundaries, pores are preferentially placed, coarsening of the microstructure occurs and there is higher Si content, leading to that area being less ductile and less resistant to crack propagation

The Noether\u2013Lefschetz locus of surfaces in toric threefolds

The Noether-Lefschetz theorem asserts that any curve in a very general surface (Formula presented.) in (Formula presented.) of degree (Formula presented.) is a restriction of a surface in the ambient space, that is, the Picard number of (Formula presented.) is (Formula presented.). We proved previously that under some conditions, which replace the condition (Formula presented.), a very general surface in a simplicial toric threefold (Formula presented.) (with orbifold singularities) has the same Picard number as (Formula presented.). Here we define the Noether-Lefschetz loci of quasi-smooth surfaces in (Formula presented.) in a linear system of a Cartier ample divisor with respect to a (Formula presented.)-regular, respectively 0-regular, ample Cartier divisor, and give bounds on their codimensions. We also study the components of the Noether-Lefschetz loci which contain a line, defined as a rational curve which is minimal in a suitable sense