10 citations · 39 across the 17 of their papers we have counts for
18 papers
Collapsing of -Gravitational Instantons
Yu-Shen Lin, Ryosuke Takahashi
We showed that a sequence of ALH*-gravitational instantons from pairs consisting of a weak del Pezzo surface and a smooth anti-canonical divisor towards a large complex structure l…
Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces
Tristan C. Collins, Yu-Shen Lin
We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some application…
Period domains for gravitational instantons
Tsung-Ju Lee, Yu-Shen Lin
Based on the uniformization theorems of gravitation instantons by Chen--Chen arXiv:1505.01790, Chen--Viaclovsky arXiv:2110.06498, Collins--Jacob--Lin arXiv:2111.09260, and Hein--Su…
SYZ mirror symmetry for del Pezzo surfaces and affine structures
Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperKähler rotation toward the large complex structure limit point. As…
The Torelli Theorem for Gravitational Instantons
Tristan Collins, Adam Jacob, Yu-Shen Lin
We give a short proof of the Torelli theorem for gravitational instantons, using the authors' previous construction of mirror special Lagrangian fibrations in del Pezzo sur…
Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Sam Bardwell-Evans, Man-Wai Mandy Cheung, Hansol Hong +1
We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagra…
Some Examples of Family Floer Mirrors
Man-Wai Mandy Cheung, Yu-Shen Lin
In this article, we give explicit calculations for the family Floer mirrors of some non-compact Calabi-Yau surfaces. We compare it with the mirror construction of Gross-Hacking-Kee…
The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces
Tristan C. Collins, Adam Jacob, Yu-Shen Lin
We prove a version of the Strominger-Yau-Zaslow mirror symmetry conjecture for non-compact Calabi-Yau surfaces arising from, on the one hand, pairs of a del…
Enumerative Geometry of Del Pezzo Surfaces
Yu-Shen Lin
We prove an equivalence between the superpotential defined via tropical geometry and Lagrangian Floer theory for special Lagrangian torus fibres in del Pezzo surfaces constructed b…
On the Complex Affine Structures of SYZ Fibration of Del Pezzo Surfaces
Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin
Given any smooth cubic curve , we show that the complex affine structure of the special Lagrangian fibration of constructed by Co…
Decomposition of Lagrangian classes on K3 surfaces
Kuan-Wen Lai, Yu-Shen Lin, Luca Schaffler
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in ter…
Special Lagrangian submanifolds of log Calabi-Yau manifolds
Tristan C. Collins, Adam Jacob, Yu-Shen Lin
We study the existence of special Lagrangian submanifolds of log Calabi-Yau manifolds equipped with the complete Ricci-flat Kähler metric constructed by Tian-Yau. We prove that if…
Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period
Hansol Hong, Yu-Shen Lin, Jingyu Zhao
We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for…
On the Tropical Discs Counting on Elliptic K3 Surfaces with General Singular Fibres
Yu-Shen Lin
Using Lagrangian Floer theory, we study the tropical geometry of K3 surfaces with general singular fibres. In particular, we give the local models for the type , , a…
Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces
Yu-Shen Lin
We prove that the open Gromov-Witten invariants on K3 surfaces satisfy the Kontsevich-Soibelman wall-crossing formula. One one hand, this gives a geometric interpretation of the sl…
Reduced Open Gromov-Witten Invariants on K3 Surfaces and Multiple Cover Formula
Yu-Shen Lin
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 der…
Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
Yu-Shen Lin
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 betwe…
Reduced Open Gromov-Witten Invariants on HyperKäher Manifolds
Yu-Shen Lin
We use the hyperKäler geometry define an disc-counting invariants with deformable boundary condition on hyperKähler manifolds. Unlike the reduced Gromov-Witten invariants, these in…