# Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations

@article{Rossi2008GromovWittenTO,
title={Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations},
author={Paolo Rossi},
journal={Mathematische Annalen},
year={2008},
volume={348},
pages={265-287}
}
• P. Rossi
• Published 19 August 2008
• Mathematics
• Mathematische Annalen
We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of $${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}$$, i.e., the complex projective line with a orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family of (polynomial) Frobenius manifolds and integrable systems of Hamiltonian PDEs, which extend the (dispersionless) bigraded Toda hierarchy (Carlet, The extended bigraded toda hierarchy. arXiv preprint…
Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies
• Mathematics
• 2016
We construct an integrable hierarchy in the form of Hirota quadratic equations (HQE) that governs the Gromov--Witten (GW) invariants of the Fano orbifold projective curve
The Local Gromov–Witten Theory of $${\mathbb{C}\mathbb{P}^1}$$ and Integrable Hierarchies
In this paper we begin the study of the relationship between the local Gromov–Witten theory of Calabi–Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first
INTEGRABLE SYSTEMS AND MODULI SPACES OF CURVES
This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and
Integrable systems and holomorphic curves
In this paper we attempt a self-contained approach to infinite dimensional Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten theory. It consists of two parts. The first
Riemann surfaces, integrable hierarchies, and singularity theory
In 1991, a celebrated conjecture of Witten [Wi1] asserted that the intersection theory of Deligne-Mumford moduli space is governed by KdVhierarchies. His conjecture was soon proved by Kontsevich
Contact homology of $S^1$-bundles over some symplectically reduced orbifolds
In this paper, we compute contact homology of some quasi-regular contact structures, which admit Hamiltonian actions of Reeb type of Lie groups. We will discuss the toric contact case, (where the
E8 spectral curves
• A. Brini
• Mathematics
Proceedings of the London Mathematical Society
• 2020
I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the
On Gromov – Witten invariants of P 1
• Mathematics
• 2019
Here, (Σg, p1, . . . , pn) denotes an algebraic curve of genus g with at most double-point singularities as well as with the distinct marked points p1, . . . , pn, and the equivalence relation ∼ is
Equivariant GW Theory of Stacky Curves
We extend Okounkov and Pandharipande’s work on the equivariant Gromov–Witten theory of $${\mathbb{P}^1}$$P1 to a class of stacky curves $${\mathcal{X}}$$X. Our main result uses virtual localization

## References

SHOWING 1-10 OF 28 REFERENCES
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Mathematics
• 2001
We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the
The extended bigraded Toda hierarchy
We generalize the Toda lattice hierarchy by considering N + M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that
The spaces of Laurent polynomials, $\mathbb{P}^1$-orbifolds, and integrable hierarchies
• Mathematics
• 2006
Let $M_{k,m}$ be the space of Laurent polynomials in one variable $x^k + t_1 x^{k-1}+... t_{k+m}x^{-m},$ where $k,m\geq 1$ are fixed integers and $t_{k+m}\neq 0$. According to B. Dubrovin \cite{D},
Extended affine Weyl groups and Frobenius manifolds
• Mathematics
Compositio Mathematica
• 1998
We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem for their
Weighted Projective Lines Associated to Regular Systems of Weights of Dual Type
We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a
Painleve transcendents in two-dimensional topological eld theory
This paper is devoted to the theory of WDVV equations of associativity. This remarkable system of nonlinear differential equations was discovered by E. Witten [85]and R. Dijkgraaf, E. Verlinde, and
Symplectic field theory and its applications
Symplectic field theory (SFT) attempts to approach the theory of holomorphic curves in symplectic manifolds (also called Gromov-Witten theory) in the spirit of a topological field theory. This
Introduction to Symplectic Field Theory
• Mathematics
• 2000
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds