scholarly journals Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants

2011 ◽  
Vol 147 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Markus Reineke
Keyword(s):  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Functional Equations ◽  
Euler Characteristics ◽  
System Of Functional Equations ◽  
Representations Of Quivers ◽  
Wall Crossing

AbstractA system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson–Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

scholarly journals Instantons, Topological Strings, and Enumerative Geometry

2010 ◽  
Vol 2010 ◽  
pp. 1-70 ◽  
Author(s):  
Richard J. Szabo
Keyword(s):  
Moduli Spaces ◽  
Gauge Theories ◽  
Topological String ◽  
Two Dimensions ◽  
Enumerative Geometry ◽  
Topological String Theory ◽  
Euler Characteristics ◽  
Wall Crossing ◽  
Supersymmetric Gauge ◽  
Torsion Free

We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe how the instanton counting in these gauge theories is related to the computation of the entropy of supersymmetric black holes and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

MEASURES OF LOCAL ENTROPIES FOR COMPOSITIVE FUZZY PARTITIONS

2011 ◽  
Vol 19 (04) ◽  
pp. 717-728 ◽  
Author(s):  
DORETTA VIVONA ◽  
MARIA DIVARI
Keyword(s):  
Functional Equations ◽  
Fuzzy Measure ◽  
System Of Functional Equations ◽  
Locality Property ◽  
Fuzzy Measures ◽  
Fuzzy Partitions

The aim of this paper is to characterize of the measures of entropies without probability or fuzzy measure for compositive fuzzy partitions, taking into account the so-called locality property. We propose a system of functional equations, whose solutions give some forms of entropies without probability or fuzzy measures.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

scholarly journals On the non-divisorial base locus of big and nef line bundles on K3[2]-type varieties

2020 ◽  
pp. 1-27
Author(s):  
Ulrike Rieß
Keyword(s):  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Ample Line Bundle ◽  
Base Point ◽  
K3 Surfaces ◽  
Line Bundles ◽  
Codimension Two ◽  
Base Locus ◽  
Base Loci ◽  
Symplectic Varieties

Abstract We approach non-divisorial base loci of big and nef line bundles on irreducible symplectic varieties. While for K3 surfaces, only divisorial base loci can occur, nothing was known about the behaviour of non-divisorial base loci for more general irreducible symplectic varieties. We determine the base loci of all big and nef line bundles on the Hilbert scheme of two points on very general K3 surfaces of genus two and on their birational models. Remarkably, we find an ample line bundle with a non-trivial base locus in codimension two. We deduce that, generically in the moduli spaces of polarized K3[2]-type varieties, the polarization is base point free.

scholarly journals Local BPS Invariants: Enumerative Aspects and Wall-Crossing

2018 ◽  
Vol 2020 (17) ◽  
pp. 5450-5475 ◽  
Author(s):  
Jinwon Choi ◽  
Michel van Garrel ◽  
Sheldon Katz ◽  
Nobuyoshi Takahashi
Keyword(s):  
Projective Space ◽  
Euler Characteristic ◽  
Moduli Spaces ◽  
Del Pezzo Surfaces ◽  
Arithmetic Genus ◽  
One Dimensional ◽  
Wall Crossing ◽  
Bps Invariants ◽  
Del Pezzo ◽  
Dimensional Projective Space

Abstract We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincaré polynomials of the moduli spaces for the curve classes $\beta $ having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of $((-K_S).\beta -1)$-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

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