The Hilbert modular group, resolution of the singularities at the cusps and related problems
The Hilbert Modular Surface for the Ideal (...5) and the Horrocks-Mumford Bundle.
The Hilbert Modular Surface of a Real Quadratic Field.
The Hodge Conjecture for a Certain Class of Fourfolds.
The Hodge Conjecture for Fermat Varieties.
The horizontal base locus of multiples of tautological sheaves of projectivised cotangent bundles.
The Horrocks-Mumford Bundle and the Ferrand Construction.
The Horrocks-Mumford bundle restricted to planes.
We study the behavior of the Horrocks-Mumford bundle FHM when restricted to a plane P2 ⊂ P4, looking for all possible minimal free resolutions for the restricted bundle. To each of the 6 resolutions (4 stable and 2 unstable) we find, we then associate a subvariety of the Grassmannian G(2,4) of planes in P4. We thus obtain a filtration of the Grassmannian, which we describe in the second part of this work.
The hyperosculating spaces of hypersurfaces.
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.