This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an em...This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.展开更多
In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande...In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande’s relative/absolute correspondence to relative-divisor/absolute correspondence.Then,we use it to lift a minimal uniruled invariant of a divisor to that of the ambient manifold.展开更多
We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher gen...We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.展开更多
The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors ...The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.展开更多
文摘This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.
文摘In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande’s relative/absolute correspondence to relative-divisor/absolute correspondence.Then,we use it to lift a minimal uniruled invariant of a divisor to that of the ambient manifold.
文摘We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.
基金supported by Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100181110071)National Natural Science Foundation of China (Grant No. 11071176),supported by National Natural Science Foundation of China (Grant Nos. 11071173 and 11221101)Hundred Talents Program for Young Teachers (Grant No. SWJTU12BR028)
文摘The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.
