Minimal models of algebraic threefolds : Mori's program
Shafarevich maps and plurigenera of algebraic varieties.
Effective base point freeness.
Toward moduli of singular varieties
Extremal rays on smooth threefolds
Real algebraic threefolds I. Terminal singularities.
The aim of this series of papers is to develop the theory of minimal models for real algebraic threefolds. The ultimate aim is to understand the topology of the set of real points of real algebraic threefolds. We pay special attention to 3–folds which are birational to projective space and, more generally, to 3–folds of Kodaira dimension minus infinity.present work contains the beginning steps of this program. First we classify 3–dimensional terminal singularities over any field of characteristic...
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Automorphism Groups of Algebraic Number Fields.
Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
We determine all anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. Many of these admit a Kähler-Einstein metric and most of them do not have tigers.
Rationally connected varieties over local fields.
Polynomials with integral coefficients, equivalent to a given polynomial.
The Nash conjecture for threefolds.
Fano hypersurfaces in weighted projective 4-spaces.
Einstein metrics on exotic spheres in dimensions 7, 11 and 15.
Page 1