The Two Most Algebraic K3 Surfaces.
The underlying real algebraic structure of complex elliptic curves.
The Uniform Position Principle for Curves in Characteristic p.
The universal periods of curves and the Schottky problem
The universal rank-(n-1) bundle on G(i,n) restricted to subvarieties.
We classify those smooth (n-1)-folds in G(1,Pn) for which the restriction of the rank-(n-1) universal bundle has more than n+1 independent sections. As an application, we classify also those (n-1)-folds for which that bundle splits.
The universal tropicalization and the Berkovich analytification
Given an integral scheme over a non-archimedean valued field , we construct a universal closed embedding of into a -scheme equipped with a model over the field with one element (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of by previous work of the authors, and we show that the set-theoretic tropicalization of with respect to this universal embedding is the Berkovich analytification . Moreover, using the scheme-theoretic...
The universal vectorial Bi-extension and p-adic heights.
The use of Schubert polynomials in SYMCHAR.
The vanishing invariants in intersection homology of complex spaces
The vanishing of the cohomology of the Orlik-Solomon algebras.
The variety of an indecomposable module is connected.
The variety of dual mock-Lie algebras
We classify all complex - and -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex -dimensional dual mock-Lie algebras.
The Waring loci of ternary quartics.
The weak 1-positivity of direct image sheaves.
The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
We study the functional codes defined on a projective algebraic variety , in the case where is a non-degenerate Hermitian surface. We first give some bounds for , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code .
The Weil pairing and the Hilbert symbol.
The Witt Group of a Smooth Complex Surface.
The Witt ring of an elliptic curve over a local field.
The work of Gross and Zagier on Heegner points and the derivatives of -series
The work of Mazur and Wiles on cyclotomic fields