119 research outputs found
Topological properties of punctual Hilbert schemes of almost-complex fourfolds (I)
In this article, we study topological properties of Voisin's punctual Hilbert
schemes of an almost-complex fourfold . In this setting, we compute their
Betti numbers and construct Nakajima operators. We also define tautological
bundles associated with any complex bundle on , which are shown to be
canonical in -theory
Block-Goettsche invariants from wall-crossing
We show how some of the refined tropical counts of Block and Goettsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative q-deformed Gromov-Witten invariants. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined
Theoretical and Experimental Investigations Regarding Open Volumetric Receivers of CRS
AbstractConcentrated sunlight is absorbed in solar thermal power plants by heat resistant absorbers and converted into usable heat which is transferred to a carrier medium. In solar tower power plants such as the plant in JĂŒlich porous absorbers can reach temperatures up to 1000°C and higher. At this power plant air as heat transfer medium is sucked in through the absorber and heated up to about 700°C. The absorber is composed of highly porous ceramic or metal wire structures. The SIJ investigates the optimization of solar absorption and the convective heat transfer to the air using thermo and fluid mechanical calculations. In such simulations the key quantities are the penetration depth of solar radiation Îș and the volumetric heat transfer coefficient αv, which indicates how much energy - depending on the volume and temperature difference - is transferred by convection between solid and fluid. The attenuation of the radiation into the depth of the absorber is described generally by an exponential function with parameter Îș. This is accompanied by heat transfer to the structure. Existing models of the key quantities have been validated by experimental data
Post-imperialism, postcolonialism and beyond: towards a periodisation of cultural discourse about colonial legacies
Taking German history and culture as a starting point, this essay suggests a historical approach to reconceptualising different forms of literary engagement with colonial discourse, colonial legacies and (post-) colonial memory in the context of Comparative Postcolonial Studies. The deliberate blending of a historical, a conceptual and a political understanding of the âpostcolonialâ in postcolonial scholarship raises problems of periodisation and historical terminology when, for example, anti-colonial discourse from the colonial period or colonialist discourse in Weimar Germany are labelled âpostcolonialâ. The colonial revisionism of Germanyâs interwar period is more usefully classed as post-imperial, as are particular strands of retrospective engagement with colonial history and legacy in British, French and other European literatures and cultures after 1945. At the same time, some recent developments in Francophone, Anglophone and German literature, e.g. Afropolitan writing, move beyond defining features of postcolonial discourse and raise the question of the post-postcolonial
Crystal melting on toric surfaces
We study the relationship between the statistical mechanics of crystal
melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric
surfaces. We argue that, in contrast to their six-dimensional cousins, the two
problems are related but not identical. We develop a vertex formalism for the
crystal partition function, which calculates a generating function for the
dimension 0 and 1 subschemes of the toric surface, and describe the
modifications required to obtain the corresponding gauge theory partition
function.Comment: 30 pages; v2: references adde
Crossings, Motzkin paths and Moments
Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain
-analogues of Laguerre and Charlier polynomials. The moments of these
orthogonal polynomials have combinatorial models in terms of crossings in
permutations and set partitions. The aim of this article is to prove simple
formulas for the moments of the -Laguerre and the -Charlier polynomials,
in the style of the Touchard-Riordan formula (which gives the moments of some
-Hermite polynomials, and also the distribution of crossings in matchings).
Our method mainly consists in the enumeration of weighted Motzkin paths, which
are naturally associated with the moments. Some steps are bijective, in
particular we describe a decomposition of paths which generalises a previous
construction of Penaud for the case of the Touchard-Riordan formula. There are
also some non-bijective steps using basic hypergeometric series, and continued
fractions or, alternatively, functional equations.Comment: 21 page
Refined Topological Vertex and Instanton Counting
It has been proposed recently that topological A-model string amplitudes for
toric Calabi-Yau 3-folds in non self-dual graviphoton background can be
caluculated by a diagrammatic method that is called the ``refined topological
vertex''. We compute the extended A-model amplitudes for SU(N)-geometries using
the proposed vertex. If the refined topological vertex is valid, these
computations should give rise to the Nekrasov's partition functions of N=2
SU(N) gauge theories via the geometric engineering. In this article, we verify
the proposal by confirming the equivalence between the refined A-model
amplitude and the K-theoretic version of the Nekrasov's partition function by
explicit computation.Comment: 22 pages, 6 figures, minor correction
D3-instantons, Mock Theta Series and Twistors
The D-instanton corrected hypermultiplet moduli space of type II string
theory compactified on a Calabi-Yau threefold is known in the type IIA picture
to be determined in terms of the generalized Donaldson-Thomas invariants,
through a twistorial construction. At the same time, in the mirror type IIB
picture, and in the limit where only D3-D1-D(-1)-instanton corrections are
retained, it should carry an isometric action of the S-duality group SL(2,Z).
We prove that this is the case in the one-instanton approximation, by
constructing a holomorphic action of SL(2,Z) on the linearized twistor space.
Using the modular invariance of the D4-D2-D0 black hole partition function, we
show that the standard Darboux coordinates in twistor space have modular
anomalies controlled by period integrals of a Siegel-Narain theta series, which
can be canceled by a contact transformation generated by a holomorphic mock
theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte
Enumerative geometry of Calabi-Yau 4-folds
Gromov-Witten theory is used to define an enumerative geometry of curves in
Calabi-Yau 4-folds. The main technique is to find exact solutions to moving
multiple cover integrals. The resulting invariants are analogous to the BPS
counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold
invariants to be integers and expect a sheaf theoretic explanation.
Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including
the sextic Calabi-Yau in CP5, are also studied. A complete solution of the
Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation.Comment: 44 page
Stability and duality in N=2 supergravity
The BPS-spectrum is known to change when moduli cross a wall of marginal
stability. This paper tests the compatibility of wall-crossing with S-duality
and electric-magnetic duality for N=2 supergravity. To this end, the
BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of
Calabi-Yau moduli space. Partition functions are presented, which capture the
stability of BPS-states corresponding to two constituents with primitive
charges and supported on very ample divisors in a compact Calabi-Yau. These
functions are `mock modular invariant' and therefore confirm S-duality.
Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to
break the `spectral flow' symmetry of the N=(4,0) CFT, which captures the
degrees of freedom of a single constituent.Comment: 25 pages + appendix; v3: final versio
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