Learn More
We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes(More)
We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties (X, L); in particular for K-and Chow stability. For each type of stability this leads to a concept of slope µ for varieties and their subschemes; if (X, L) is semistable then µ(Z) ≤ µ(X) for all Z ⊂ X. We give examples such as(More)
1 Introduction Calabi–Yau m-folds are compact Ricci-flat Kähler manifolds (M, J, g) of complex dimension m, with trivial canonical bundle K M. Taken together, the complex structure J, Kähler metric g, and a holomorphic section Ω of K M make up a rich, fairly rigid geometrical structure with very interesting properties — for instance, Calabi–Yau m-folds(More)
We find stability conditions ([D2], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the(More)
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian sub-manifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case(More)