Higher genus symplectic invariants and sigma model coupled with gravity

Yongbin Ruan; Gang Tian

doi:10.1007/s002220050192

Home/Archive/arXiv

arXiv · alg-geom/9601005

Higher genus symplectic invariants and sigma model coupled with gravity

Yongbin Ruan·Gang Tian

View original source ↗Read source document ↗Export metadata ↓

Abstract

We define higher genus Gromov-Witten invariants and establish a mathematical theory of sigma model coupled with gravity over any semi-positive symplectic manifolds. As applications, we verify the stablizing conjecture of symplectic 4-manifolds for simply connected elliptic surfaces and construct smooth 6-manifolds admitting infinitely many deformation classes of symplectic structures.

Explore related subjects

alg-geom dg-ga hep-th math.AG math.DG

Keep this discovery

BibTeX RIS

Yongbin Ruan, Gang Tian. 1996-01-06. Higher genus symplectic invariants and sigma model coupled with gravity. https://doi.org/10.1007/s002220050192

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2017

Boundedness and $K^2$ for log surfaces

Let $ε, C$ be two positive real numbers, and $\mathcal C \subset \mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \sum b_j B_j)$ denote a projective surface with an $\mathbb R$-divisor. Then (1) The class $\{X\}$ of surfaces for which there exists a divisor $B$ such that $(X,B)$ is $ε$-log terminal and $-(K_X + B)$ is nef (excluding only those for which at the same time $K_X\equiv 0$, $B=0$, and $X$ has at worst Du Val singularities), is bounded. (2) The set $\{(K_X + B)^2\}$ of squares for the semi log canonical pairs $(X, B)$ with ample $K_X + B$ and $b_j \in \mathcal C$, is a DCC set. (3) The class $\{(X,B)\}$ of pairs such that $(X, B)$ is semi log canonical, $K_X + B$ is ample, $(K_X + B)^2 = C$ and $b_j \in \mathcal C$, is bounded.

alg-geom↗

arXiv2015

Quotients par des groupes non réductifs et variétés de modules de complexes

I give a way to construct moduli spaces of complexes, as quotients of open subsets of the space of all complexes by the product of the groups of automorphisms of the terms.

alg-geom↗

arXiv2014

Plane Curves with Hyperbolic and C-hyperbolic Complements

The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a Carathéodory hyperbolic covering. We study here the plane projective curves whose complements are C--hyperbolic. For instance, we show that most of the curves whose duals are nodal or, more generally, immersed curves, belong to this class. We also give explicit examples of irreducible such curves of any even degree d greater or equal 6.

alg-geom↗