The Laplacian for a Frobenius manifold

2004 ◽  
pp. 321-339
Author(s):  
Ikuo Satake
Keyword(s):  
Frobenius Manifold

scholarly journals SOME REMARKS ON LANDAU–GINZBURG POTENTIALS FOR ODD-DIMENSIONAL QUADRICS

2014 ◽  
Vol 57 (3) ◽  
pp. 481-507 ◽  
Author(s):  
VASSILY GORBOUNOV ◽  
MAXIM SMIRNOV
Keyword(s):  
Initial Conditions ◽  
Quantum Cohomology ◽  
Frobenius Manifold

AbstractWe study the possibility of constructing a Frobenius manifold for the standard Landau–Ginzburg model of odd-dimensional quadrics Q2n+1 and matching it with the Frobenius manifold attached to the quantum cohomology of these quadrics. Namely, we show that the initial conditions of the quantum cohomology Frobenius manifold of the quadric can be obtained from the suitably modified standard Landau–Ginzburg model.

scholarly journals Open Saito Theory for A and D Singularities

2020 ◽  
Author(s):  
Alexey Basalaev ◽  
Alexandr Buryak
Keyword(s):  
Parameter Space ◽  
Moduli Space ◽  
Homogeneous Polynomial ◽  
Coxeter Groups ◽  
Frobenius Manifold ◽  
Simple Singularity ◽  
Universal Unfolding ◽  
Wdvv Equations ◽  
Manifold Structure ◽  
Frobenius Manifolds

Abstract A well-known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper, we present a generalization of this construction for the singularities of types $A$ and $D$ that gives a solution of the open WDVV equations. For the $A$-singularity, the resulting solution describes the intersection numbers on the moduli space of $r$-spin disks, introduced recently in a work of the 2nd author, E. Clader and R. Tessler. In the 2nd part of the paper, we describe the space of homogeneous polynomial solutions of the open WDVV equations associated to the Frobenius manifolds of finite irreducible Coxeter groups.

scholarly journals DUBROVIN’S SUPERPOTENTIAL AS A GLOBAL SPECTRAL CURVE

2017 ◽  
Vol 18 (3) ◽  
pp. 449-497 ◽  
Author(s):  
P. Dunin-Barkowski ◽  
P. Norbury ◽  
N. Orantin ◽  
A. Popolitov ◽  
S. Shadrin
Keyword(s):  
Field Theory ◽  
Spectral Curve ◽  
Frobenius Manifold ◽  
Simple Point ◽  
Topological Recursion ◽  
Cohomological Field Theory

We apply the spectral curve topological recursion to Dubrovin’s universal Landau–Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differentials reproduces the cohomological field theory associated with the same point of the initial Frobenius manifold.

scholarly journals Linear free divisors and Frobenius manifolds

2009 ◽  
Vol 145 (5) ◽  
pp. 1305-1350 ◽  
Author(s):  
Ignacio de Gregorio ◽  
David Mond ◽  
Christian Sevenheck
Keyword(s):  
Frobenius Manifold ◽  
Base Space ◽  
Linear Functions ◽  
Universal Unfolding ◽  
Manifold Structure ◽  
Frobenius Manifolds ◽  
Free Divisors

AbstractWe study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.

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