The infinitesimal and generalized Hodge Conjecture for some families of sextic threefolds.
The irreducible components of moduli spaces of vector bundles on surfaces.
The Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The irregularity of ruled surfaces in three dimensional projective space.
Let S be a ruled surface in P3 with no multiple generators. Let d and q be nonnegative integers. In this paper we determine which pairs (d,q) correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in P5.
The Kähler cone on Calabi-Yau threefolds.
The Kähler cone on Calabi-Yau threefolds (Erratum).
The Kähler Ricci flow on Fano manifolds (I)
We study the evolution of pluri-anticanonical line bundles along the Kähler Ricci flow on a Fano manifold . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of . For example, the Kähler Ricci flow on converges when is a Fano surface satisfying or . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....
The Kodaira dimension of certain moduli spaces of abelian surfaces
The KSBA compactification for the moduli space of degree two pairs
Inspired by the ideas of the minimal model program, Shepherd-Barron, Kollár, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest examples that fits into this framework: the case of pairs consisting of a degree two surface and an ample divisor . Specifically, we construct and describe explicitly a geometric compactification for the moduli of degree two pairs. This compactification...
The Local Nash problem on arc families of singularities
This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.
The mathematics of fivebranes.
The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Milnor number of functions on singular hypersurfaces
The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical...
The Modell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3.
The modularity of the Barth-Nieto quintic and its relatives.
The moduli and the global period mapping of surfaces with : a counterexample to the global Torelli problem
The Moduli of Weierstrass Fibriations Over P1 .
The Moduli Space of (3,3,3) Trilinear forms.
The Moduli Space of 3-Folds with K = 0 may Nevertheless be Irreducible.
The moduli space of special lagrangian submanifolds