Lagrangian Constant Cycle Subvarieties in Lagrangian Fibrations
نویسندگان
چکیده
منابع مشابه
Lagrangian subvarieties of abelian fourfolds
Let (W, ω) be a smooth projective algebraic variety of dimension 2n over C together with a holomorphic (2, 0)-form of maximal rank 2n. A subvariety X ⊂ W is called weakly lagrangian if dim X ≤ n and if the restriction of ω to X is trivial (notice that X can be singular). An n-dimensional subvariety X ⊂ W with this property is called lagrangian. For example, any curve C contained in a K3 or abel...
متن کاملOn Deformations of Lagrangian Fibrations
Let X be an irreducible symplectic manifold and Def(X) the Kuranishi space. Assume that X admits a Lagrangian fibration. We prove that X can be deformed preserving a Lagrangian fibration. More precisely, there exists a smooth hypersurface H of Def(X) such that the restriction family X ×Def(X) H admits a family of Lagrangian fibrations over H.
متن کاملSpecial Lagrangian Fibrations II: Geometry
This paper is a progress report on work surrounding the Strominger-Yau-Zaslow mirror symmetry conjecture [25]. Roughly put, this conjecture suggests the following program for attacking an appropriate form of the mirror conjecture. Let X be a Calabi-Yau n-fold, with a large complex structure limit point p in a compactification of the complex moduli space of X . One expects mirrors of X to be ass...
متن کاملDeformations of holomorphic Lagrangian fibrations
Let X → Pn be a 2n-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over Pn. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space Def(X) of deformations of X. We extend his result by proving that if the Lagrangian fibration admits a section, then there is a codimension two family of deformations which also pr...
متن کاملExamples of Special Lagrangian Fibrations
Of late there has been a great deal of interest in special Lagrangian submanifolds and manifolds fibred in special Lagrangian submanifolds, motivated by the Strominger-Yau-Zaslow conjecture [29]. One of the basic approaches to finding examples is to exploit symmetries of the ambient manifold. If X is a (non-compact) n-dimensional Calabi-Yau manifold with Kähler form ω and nowhere vanishing holo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2018
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx334