Algebro-geometric analogues of Donaldson's polynomials.
Algorithms for the computation of moduli spaces for semiquasihomogeneous singularities.
We present algorithms and their implementation in the computer algebra system Singular 2.0 for the computation of equations for moduli spaces for semiquasihomogeneous singularities w.r.t. right equivalence. In addition, we describe the structure of the stabilizer group of Brieskorn-Pham singularities.
Amibes de variétés algébriques et dénombrement de courbes
Les amibesdes variétés algébriques dans sont les images de ces variétés par l’application des moments , . Des résultats obtenus par G. Mikhalkin montrent l’utilité des amibes pour l’étude des variétés algébriques réelles et complexes. Les amibes peuvent être déformées en des complexes polyédraux appelésvariétés algébriques tropicales. Cette déformation permet, en particulier, de calculer les invariants de Gromov-Witten du plan projectif et d’autres surfaces toriques en dénombrant des courbes...
Ample and spanned vector bundles of sectional genera three.
Ample Cartier divisors on normal surfaces.
Ample line bundles on blown up surfaces.
Ample line bundles on smooth surfaces.
Ample vector bundles with sections vanishing along conic fibrations over curves.
Ample vector bundles with zero loci having a bielliptic curve section.
An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
An arithmetic characterisation of the symmetric monodromy groups of singularities.
An elliptic surface of Mordell-Weil rank over the rational numbers
Néron showed that an elliptic surface with rank , and with base , and geometric genus , may be obtained by blowing up points in the plane. In this paper, we obtain parameterizations of the coefficients of the Weierstrass equations of such elliptic surfaces, in terms of the points. Manin also describes bases of the Mordell-Weil groups of these elliptic surfaces, in terms of the points ; we observe that, relative to the Weierstrass form of the equation,(with , and a basis can be found...
An example of an asymptotically Chow unstable manifold with constant scalar curvature
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
An example of two homeomorphic, nondiffeomorphic complete intersection surfaces.
An Example of Unirational Surfaces in Characteristic p.
An exotic smooth structure on .
An extension of the Apéry number supercongruence
An improved bound for the degree of smooth surfaces in not of general type
An obstruction for smoothing of Gorenstein surface singularities.
Anticanonical Models of Rational Surfaces.