Let $C$ be an irreducible smooth complex projective curve of genus $g\geq 2$ and let $C\_d$ its $d$-fold symmetric product. In this paper, we study the question semi-orthogonal decompositions derived category $C\_d$. This entails investigations canonical system on $C\_d$, in particular base locus.

The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

We prove that there exists a positive integer νn depending only on n such that for every smooth projective n-fold of general type X defined over C, | mKX | gives a birational rational map from X into a projective space for every m ≥ νn. This paper is a concise and refined version of [17]. MSC 32J25

We give an elementary explicit construction of cell decomposition of the mod-uli space of projective structures on a two dimensional surface, analogous to the decomposition of Penner/Strebel for moduli space of complex structures. The relations between projective structures and P GL(2, C) flat connections are also described.

We prove that there exists a positive integer νn depending only on n such that for every smooth projective n-fold of general type X defined over C, | mKX | gives a birational rational map from X into a projective space for every m ≥ νn. This paper is a concise and refined version of [17]. MSC 32J25

The natural mapping of the right quaternion vector space H onto the quaternion projective line (identified with the four-sphere) can be defined for complex quaternions H ⊗R C as well. We discuss its exceptional set, the fiber subspaces, and how the linear automorphism groups of two-dimensional quaternion vector spaces and modules induce groups of projective automorphisms of the image quadrics.

Suppose ∆C,E ∼= e. A central problem in discrete model theory is the classification of elements. We show that there exists a meager and Hamilton contra-infinite, projective number. We wish to extend the results of [15] to linearly projective subgroups. U. Desargues’s classification of pointwise open hulls was a milestone in constructive measure theory.

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

Let k be a field, X a smooth projective surface over k, Y a smooth projective curve over k, and f : X → Y a generically smooth semistable curve of genus g ≥ 2 over Y . Let K be the function field of Y , K the algebraic closure of K, and C the generic fiber of f . For D ∈ Pic(C)(K), let jD : CK → Pic 0(C)K be an embedding defined by jD(x) = x − D. Then, we have the following conjecture due to Bo...

We study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c...