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 .
The automorphism group of
The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .
The average distribution of cubic exponential sums.
The Bauer Group of a Rational Surface.
The Behaviour of the Plurigenera of Surfaces Under Algebraic Smooth Deformations.
The Betten-Walker spread and Cayley's ruled cubic surface.
The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface.
The Bifurcation Set and Logarithmic Vector Fields.
The Birational Geometry of Surfaces with Rational Double Points.
The border cases of the lifting theorem for surfaces in P4.