scholarly journals Partition Functions of $$\mathcal{N}=(2,2)$$ Supersymmetric Sigma Models and Special Geometry on the Moduli Spaces of Calabi-Yau Manifolds

2019 ◽  
Vol 201 (2) ◽  
pp. 1606-1613 ◽  
Author(s):  
A. A. Belavin ◽  
B. A. Eremin
Keyword(s):  
Sigma Models ◽  
Moduli Spaces ◽  
Partition Functions ◽  
Special Geometry ◽  
Calabi Yau Manifolds

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

scholarly journals Counting curves on surfaces

2017 ◽  
Vol 28 (02) ◽  
pp. 1750012
Author(s):  
Norman Do ◽  
Musashi A. Koyama ◽  
Daniel V. Mathews
Keyword(s):  
Moduli Spaces ◽  
Symplectic Geometry ◽  
Differential Forms ◽  
Combinatorial Problem ◽  
Partition Functions ◽  
Low Dimensional Topology ◽  
Moduli Spaces Of Curves ◽  
Finite Set ◽  
Curves On Surfaces ◽  
Low Dimensional

We consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology: for a compact surface [Formula: see text], with a finite set of points [Formula: see text] fixed on its boundary, how many configurations of disjoint arcs are there on [Formula: see text] whose boundary is [Formula: see text]? We find that this enumerative problem, counting curves on surfaces, has a rich structure. We show that such curve counts obey an effective recursion, in the general spirit of topological recursion, and exhibit quasi-polynomial behavior. This “elementary curve-counting” is in fact related to a more advanced notion of “curve-counting” from algebraic geometry or symplectic geometry. The asymptotics of this enumerative problem are closely related to the asymptotics of volumes of moduli spaces of curves, and the quasi-polynomials governing the enumerative problem encode intersection numbers on moduli spaces. Among several other results, we show that generating functions and differential forms for these curve counts exhibit structure that is reminiscent of the mathematical physics of free energies, partition functions and quantum curves.

scholarly journals The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity

1997 ◽  
Vol 12 (06) ◽  
pp. 381-392 ◽  
Author(s):  
Mitsuko Abe
Keyword(s):  
Partition Function ◽  
Gravity Model ◽  
Moduli Spaces ◽  
Partition Functions ◽  
K3 Surface ◽  
Analytic Manifold ◽  
Rham Complex ◽  
De Rham ◽  
Complex Analytic Manifold ◽  
Equivalent Class

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some [Formula: see text]-torsions. [Formula: see text]-torsion is the extension of R-torsion for the de Rham complex to that for the [Formula: see text]-complex of a complex analytic manifold.

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