Symmetric functions and the Chern characters of a hypersurface with singularities
Symmetric homology planes.
Symmetrische Modulflächen der Diskriminante p2.
Symplectic involutions on deformations of K3[2]
Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert...
Symplectic structure of the moduli space of sheaves on an abelian or K3 surface.
Symplectic structures on moduli spaces of framed sheaves on surfaces
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.
Syzygies and Koszul cohomology of smooth projective varieties for arbitrary dimension.
Syzygies and the Abel-Jacobi map for cyclic coverings.
Syzygies of abelian surfaces embedded in ... (...).
Tangencies of generic real projective hypersurfaces.
Tensor product theorem for Hitchin pairs – An algebraic approach
We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields of characteristic zero and characteristic , with satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.
The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree 14.
The Abel-Jacobi mapping for the quartic threefold.
The additive group actions on -homology planes
In this article, we prove that a -homology plane with two algebraically independent -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface in the affine -space via a free -action, where is the order of a finite group .
The adjunction mapping and hyperelliptic divisors on a surface.
The algebraic geometry of representation spaces associated to Seifert fibered homology 3-spheres.
The Arithmetic Genus of the Hubert Modular Variety and the Elliptic Fixed Points of the Hilbert Modular Group.
The arithmetic of certain del Pezzo surfaces and K3 surfaces
We construct del Pezzo surfaces of degree violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.
The arithmetic of zero cycles on surfaces with geometric genus and irregularity zero.
The automorphism group of linear sections of the Grassmannians .