4 papers
K-semistability and singularities of normal affine cones
Tran-Trung Nghiem
We provide a complete and optimal characterization of -Gorenstein normal affine singularities in terms of their K-stability in the sense of Collins--Székelyhidi.
Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
Ronan J. Conlon, Tran-Trung Nghiem
We present infinitely many new examples of affine Calabi--Yau manifolds of Euclidean volume growth and quadratic curvature decay, whose tangent cones at infinity are irregular and…
Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity
Tran-Trung Nghiem
We show that on every non- complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent…
On the regularity of conical Calabi-Yau potentials
Tran-Trung Nghiem
Using pluripotential theory on degenerate Sasakian manifolds, we show that a locally bounded conical Calabi-Yau potential on a Fano cone is actually smooth on the regular locus. Th…