arXiv subjects

Changzheng Li

Publications and source records attributed to Changzheng Li.

38 records · Page 3Linked to original sources

arXiv2010

Functorial relationships between quantum cohomology of complete and partial flag varieties

We give a natural filtration F on quantum cohomology QH(G/B) of G/B, which respects the quantum product structure. Its associated graded algebra is isomorphic to the tensor product of QH(G/P) and a corresponding graded algebra of QH(P/B) after localization. When the quantum parameter goes to zero, this specializes to the filtration on the classical cohomology H(G/B) from the Leray spectral sequence associated to the fibration P/B --> G/B --> G/P.

math.AG↗

arXiv2008

Hard Lefschetz actions in Riemannian geometry with special holonomy

It is known that the hard Lefschetz action, together with Kähler identities for Kähler (resp. hyperkähler) manifolds, determines a $\mathfrak{su}(1,1)_{sup}$ (resp. $\mathfrak{sp}(1,1)_{sup}$) Lie superalgebra action on differential forms. In this paper, we explain the geometric origin of this action, and we also generalize it to manifolds with other holonomy groups. For semi-flat Calabi-Yau (resp. hyperkähler) manifolds, these symmetries can be enlarged to a $\mathfrak{so}(2,2)_{sup}$ (resp. $\mathfrak{su}(2,2)_{sup}$) action.

math.DG↗