Arithmetical quadratic surfaces of genus 0, I.
Arithmetical quadratic surfaces of genus 0, II.
Arithmetically Gorenstein curves on arithmetically Cohen-Macaulay surfaces.
Let Sigma C PN be a smooth connected arithmetically Cohen-Macaulay surface. Then there are at most finitely many complete linear systems on Sigma, not of the type |kH - K| (H hyperplane section and K canonical divisor on Sigma), containing arithmetically Gorenstein curves.
Around real Enriques surfaces.
We present a brief overview of the classification of real Enriques surfaces completed recently and make an attempt to systemize the known classification results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular, we prove two new congruence type prohibitions on the Euler characteristic of the real part of a real algebraic surface.
Around the intersection form of an isolated singularity of hypersurface
ASD moduli spaces over four-manifolds with tree-like ends.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
Atiyah Classes and Closed Forms on Moduli Spaces of Sheaves
Auslander's Delta, the Quasihomogeneity of Isolated Hypersurface Singularities and the Tate Resolution of the Moduli Algebra.
Automorphism groups of orientable elliptic-hyperelliptic Klein surfaces.
Automorphism groups of rational elliptic surfaces with section and constant J-map
In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ⋊ Aut σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut σ (B) of the automorphisms preserving a...
Automorphisms of cusps and Inoue-Hirzebruch surfaces
Automorphisms of Enriques Surfaces.
Automorphisms of Enriques surfaces which act trivially on the cohomology groups.
Automorphisms of order three on numerical Godeaux surfaces
We prove that a numerical Godeaux surface cannot have an automorphism of order three.
Automorphisms of rational double points and moduli spaces of surfaces of general type
Babbage's Conjecture, Contact of Surfaces, Symmetric Determinantal Varieties and Applications.
Base curves of multicanonical systems on threefolds
Bases of homology spaces of the Hilbert scheme of points in an algebraic surface.
We find two basis of the spaces of rational homology of the Hilbert scheme of points in an algebraic surface, by exhibiting two candidates having as cardinalities the known Betti numbers of this scheme and showing that both intersect in a matrix of nonzero determinant.
Beispiele dreidimensionaler Hilbertscher Modulmannigfaltigkeiten von allgemeinem Typ.