The canonical filtration of higher dimensional purely elliptic singularity of a special type.
The Chow rings of smooth complete -embeddings
The classification of 4-dimensional Kähler manifolds with small eigenvalue of the Dirac operator.
The complex structure on a connected sum of S³ x S³ with trivial canonical bundle.
The cone of curves of a K3 surface.
The ?-constant stratum is not smooth.
The cylinder homomorphism associated to quintic fourfolds
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The Denef-Loeser series for toric surface singularities.
Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(H) in some suitable localization of the Grothendieck ring of algebraic...
The density of S-integral points in projective space with respect to a quadric
The determinant line bundle over moduli spaces of instantons on abelian surfaces.
The diffeomorphism classification of non-simply connected Dolgachev surfaces.
The discriminant of a real simple singularity
The distribution of bidegrees of smooth surfaces in Gr (1, P3).
The dual of the invariant quintic.
The equations of the abelian surfaces embedded in ...4 (...).
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The existence of algebraic surfaces with preassigned Chern numbers.
The existence of elliptic fibre space structures on Calabi-Yau threefolds.
The Fano surface of the Gushel threefold