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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deformation rigidity of Fano manifolds
法诺歧管 变形刚度 光滑射影品种X
2023/4/17
A smooth projective variety X is called rigid if any deformation of X is isomorphic to itself. A first example is the projective space, but in general it is a subtle and difficult problem to prove the...
Classification of 2-Fano manifolds with high index
Classification of 2-Fano manifolds high index Algebraic Geometry
2012/6/27
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
Birational superrigidity and slope stability of Fano manifolds
Birational superrigidity Fano manifolds Algebraic Geometry
2011/9/15
Abstract: We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Fano manifolds which are not slope stable along curves
Fano manifolds slope stable along curves Algebraic Geometry
2011/8/26
Abstract: We show that a Fano manifold (X,-K_X) is not slope stable with respect to a smooth curve Z if and only if (X,Z) is isomorphic to one of (projective space, line), (product of projective line ...
Anticanonical divisors and curve classes on Fano manifolds
Anticanonical divisors curve classes Fano manifolds
2010/12/6
It is well known that the Hodge conjecture with rational coefficients holds for degree 2n − 2 classes on complex projective n-folds. In this paper we study the more precise question if on a rati...