We announce here the construction of examples of smooth Calabi-Yau 3-folds in P6 of low degree, up to degree 17. In the last degree their construction is rather complicated, and parametrized by smooth septics in P2 having a a g1 d with d = 13, 12, or 10. This turns out to show the existence of three unirational components of their Hilbert scheme, all having the same dimension 23+ 48 = 71. The c...

In [2] we investigated the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice Λ(CA2) of all subvarieties of the variety CA2 of two-dimensional cylindric algebras. We give a dual characterization of representable two-dimensional cylindric algebras, prove that the cardinality of Λ(CA2) is that ...

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, b...

Sparse elimination theory concerns the study of Chow forms and discriminants associated with toric varieties, that is, subvarieties of projective space which are parametrized by monomials (Sturmfels, 1993; Gel’fand et al., 1994). This theory has its origin in the work of Gel’fand et al. on multivariate hypergeometric functions (Gel’fand et al., 1989). The singularities of these functions occur ...

Fix a nonsingular algebraic variety Y over an algebraically closed field (of arbitrary characteristic). An arrangement of subvarieties S is a finite collection of nonsingular subvarieties such that all nonempty scheme-theoretic intersections of subvarieties in S are again in S, or equivalently, such that any two subvarieties intersect cleanly and the intersection is either empty or a subvariety...

The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points flip and Neimark-Sacker , and so establish subor supercriticality of these bifurcat...

Let P be the variety of semigroups defined by the identity xyzx ≈ x. By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains...

Let M2 be the Igusa compactification of the Siegel modular variety of degree 2 and level 2. In earlier work with R. Lee, we carefully investigated this variety. Subvarieties Dl (compactification divisors) and H∆ (Humbert surface of discriminant 1) play a prominent role in its structure; in particular their fundamental classes span H4(M2;Z). We return to this variety and consider another class o...

Using deformation theory of rational curves, we prove a conjecture Sommese on the extendability morphisms from ample subvarieties when morphism is smooth (or mildly singular) fibration with rationally connected fibers. We apply this result in context Fano fibrations and classification theorem for projective bundle quadric structures subvarieties.