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Register a new userReduced Open Gromov-Witten Invariants on K3 Surfaces and Multiple Cover Formula
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Authors
Yu-Shen Lin
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In the paper, we study the wall-crossing phenomenon of reduced open Gromov-Witten invariants on K3 surfaces with rigid special Lagrangian boundary condition. As a corollary, we derived the multiple cover formula for the reduced open Gromov-Witten invariants.
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In this paper, we study holomorphic discs in K3 surfaces and defined the open Gromov-Witten invariants. Using this new invariant, we can establish a version of correspondence between tropical discs and holomorphic discs with non-trivial invariants. We give an example of wall-crossing phenomenon of the invariant and expect it satisfies Kontsevich-Soibelman wall-crossing formula.
We use the hyperKaler geometry define an disc-counting invariants with deformable boundary condition on hyperKahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon and are expected to be the generalized Donaldson-Thomas invariants in the construction of hyperKahler metric proposed by Gaiotto-Moore-Neitzke.
In this paper we exploit the geometric approach to the virtual fundamental class, due to Fukaya-Ono and Li-Tian, to compare the virtual fundamental classes of stable maps to a symplectic manifold and a symplectic submanifold whenever all constrained stable maps to the former are contained in the latter to first order. This exten
Let $(X,omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary $(Sigma,partialSigma)$ to the pair $(X,L)$ satisfying Lagrangian boundary conditions and intersecting $V$. In some special cases, for instance, under the semi-positivity condition, we study the stable moduli space of such open pseudoholomorphic maps involving the intersection data. If $Lcap V=emptyset$, we study the problem of orientability of the moduli space. Moreover, assume that there exists an anti-symplectic involution $phi$ on $X$ such that $L$ is the fixed point set of $phi$ and $V$ is $phi$-anti-invariant, then we define the so-called relatively open invariants for the tuple $(X,omega,V,phi)$ if $L$ is orientable and dim$Xle 6$. If $L$ is nonorientable, we define such invariants under the condition that dim$Xle4$ and some additional restrictions on the number of marked points on each boundary component of the domain.
Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.
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