Holomorphic cuves in Exploded Torus Fibrations: Regularity
نویسنده
چکیده
The category of exploded torus fibrations is an extension of the smooth category related to tropical geometry in which some adiabatic limits appear as smooth families. This paper contains regularity results for families of holomorphic curves in this category. The main result is a local model for the moduli space of holomorphic curves, which in the case of transversality of the ∂̄ equation implies that the moduli space of holomorphic curves has the appropriate regularity. (This includes regularity of families of holomorphic curves in the smooth category which exhibit bubbling behavior.) A sketch of one method for constructing a ‘virtual class’ for the moduli stack of holomorphic curves using these local regularity results is included.
منابع مشابه
Holomorphic curves in Exploded Torus Fibrations: Compactness
The category of exploded torus fibrations is an extension of the category of smooth manifolds in which some adiabatic limits look smooth. (For example, the type of limits considered in tropical geometry appear smooth.) In this paper, we prove a compactness theorem for (pseudo)holomorphic curves in exploded torus fibrations. In the case of smooth manifolds, this is just a version of Gromov’s com...
متن کاملExploded fibrations
Initiated by Gromov in [1], the study of holomorphic curves in symplectic manifolds has been a powerfull tool in symplectic topology, however the moduli space of holomorphic curves is often very difficult to find. A common technique is to study the limiting behavior of holomorphic curves in a degenerating family of complex structures which corresponds to a kind of adiabatic limit. The category ...
متن کاملCalibrated Fibrations on Complete Manifolds via Torus Action
In this paper we will investigate torus actions on complete manifolds with calibrations. For Calabi-Yau manifolds M with a Hamiltonian structure-preserving k-torus action we show that any symplectic reduction has a natural holomorphic volume form. Moreover Special Lagrangian (SLag) submanifolds of the reduction lift to SLag submanifolds of M , invariant under the torus action. If k = n− 1 and H...
متن کاملSpecial Lagrangian fibrations. I. Topology,” Integrable systems and algebraic geometry (Kobe/Kyoto
Yau and Zaslow made a surprising conjecture about pairs of mirror manifolds, which, if true, should at last provide a true geometric understanding of mirror symmetry. Simply put, string theory suggests that if X andˇX are mirror pairs of n-dimensional Calabi-Yau manifolds, then on X there should exist a special Lagrangian n-torus fibration f : X → B, (with some singular fibres) such thatˇX is o...
متن کاملFrom Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform
We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the transformation relates supersymmetric Aand Bcycles. In this paper, we assume that the mirror pair are dual torus fibrations with flat tori and that the A-cycle is a...
متن کامل