D5D5-brane type I superstring background fields in terms of type IIB ones by canonical method and T-duality approach

We consider type IIB superstring theory with embedded $D5$-brane and choose boundary conditions which preserve half of the initial supersymmetry. In the canonical approach that we use, boundary conditions are treated as canonical constraints. The effective theory, obtained from the initial one on the solution of boundary conditions, has the form of the type I superstring theory with embedded $D5$-brane. We obtain the expressions for $D5$-brane background fields of type I theory in terms of the $D5$-brane background fields of type IIB theory. We show that beside known $\Omega$ even fields, they contain squares of $\Omega$ odd ones, where $\Omega$ is world-sheet parity transformation, $\Omega:\sigma\to -\sigma$. We relate result of this paper and the results of [1] using T-dualities along four directions orthogonal to $D5$-brane

Lower-dimensional pure-spinor superstrings

We study to what extent it is possible to generalise Berkovits' pure-spinor construction in d=10 to lower dimensions. Using a suitable definition of a ``pure'' spinor in d=4,6, we propose models analogous to the d=10 pure-spinor superstring in these dimensions. Similar models in d=2,3 are also briefly discussed.Comment: 17 page

Higher Dimensional Elliptic Fibrations and Zariski Decompositions

We study the existence and properties of birationally equivalent models for elliptically fibered varieties. In particular these have either the structure of Mori fiber spaces or, assuming some standard conjectures, minimal models with a Zariski decomposition compatible with the elliptic fibration. We prove relations between the birational invariants of the elliptically fibered variety, the base of the fibration and of its Jacobian.Comment: 16 pages; Accepted for publication in Communications in Contemporary Mathematic