On Fano Manifolds of large index.
On Fiber Products of Rational Elliptic Surfaces with Section.
On Finite Intersections of "Henselian Valued" Fields.
On finite same-invariant linear groups.
On fixed points of automorphisms of non-orientable unbordered Klein surfaces.
On formal groups obtained from symmetric powers
On formal groups over complete discrete valuation rings with application to a theorem of Lutz.
On functional equations of complex powers.
On fundamental groups of algebraic varieties and value distribution theory
If a smooth projective variety admits a non-degenerate holomorphic map from the complex plane , then for any finite dimensional linear representation of the fundamental group of the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.
On galois automorphisms of the fundamental group of the projective line minus three points.
On Galois covers of Hirzebruch surfaces.
On Galois module structure of the cohomology groups of an algebraic variety.
On Galois representations arising from towers of coverings of P1 ... .
On Galois representations defined by torsion points of modular elliptic curves
On generalized Cauchy-Riemann equations on manifolds
On generalized Chern classes and Chern numbers of irreducible complex algebraic varieties with arbitrary singularities
On generalized “ham sandwich” theorems
In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let be subsets with finite Lebesgue measure. Then, for any sequence of -linearly independent polynomials in the polynomial ring there are real numbers , not all zero, such that the real affine variety simultaneously bisects each of subsets , . Then some its applications are studied.
On generation of jets for vector bundles.
We introduce and study the k-jet ampleness and the k-jet spannedness for a vector bundle, E, on a projective manifold. We obtain different characterizations of projective space in terms of such positivity properties for E. We compare the 1-jet ampleness with different notions of very ampleness in the literature.
On generically polarized Gorenstein surfaces of sectional genus two.
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...