XMM-Newton observations of two transient millisecond X-ray pulsars in quiescence

We report on XMM-Newton observations of two X-ray transient millisecond pulsars (XRTMSPs). We detected XTE J0929-314 with an unabsorbed luminosity of \~7x10^{31} erg/s. (0.5-10 keV) at a fiducial distance of 10 kpc. The quiescent spectrum is consistent with a simple power law spectrum. The upper limit on the flux from a cooling neutron star atmosphere is about 20% of the total flux. XTE J1807-294 instead was not detected. We can put an upper limit on the source quiescent 0.5-10 keV unabsorbed luminosity <4x10^{31} erg/s at 8 kpc. These observations strenghten the idea that XRTMSPs have quiescent luminosities significantly lower than classical neutron star transients.Comment: 4 pages including 1 figures. Accepted for publication in A&A Letter

Special Varieties and classification Theory

A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. Moreover, for any compact K\"ahler $X$ we define a fibration $c_X:X\to C(X)$, which we call its core, such that the general fibres of $c_X$ are special, and every special subvariety of $X$ containing a general point of $X$ is contained in the corresponding fibre of $c_X$. We then conjecture and prove in low dimensions and some cases that: 1) Special manifolds have an almost abelian fundamental group. 2) Special manifolds are exactly the ones having a vanishing Kobayashi pseudometric. 3) The core is a fibration of general type, which means that so is its base $C(X)$,when equipped with its orbifold structure coming from the multiple fibres of $c_X$. 4) The Kobayashi pseudometric of $X$ is obtained as the pull-back of the orbifold Kobayashi pseudo-metric on $C(X)$, which is a metric outside some proper algebraic subset. 5) If $X$ is projective,defined over some finitely generated (over $\Bbb Q$) subfield $K$ of the complex number field, the set of $K$-rational points of $X$ is mapped by the core into a proper algebraic subset of $C(X)$. These two last conjectures are the natural generalisations to arbitrary $X$ of Lang's conjectures formulated when $X$ is of general type.Comment: 72 pages, latex fil

Birational stability of the cotangent bundle

We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent sheaves are birationally stable, unless the orbifold is uniruled

Special orbifolds and birational classification: a survey

We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this special case only.} varieties $X$ into varieties (or rather ` geometric orbifolds\rq $)$ of one of the three \pure geometries determined by the `sign' (negative, zero, or positive) of the canonical bundle. These decompositions being birationally invariant, birational versions of these \pure geometries, based on the \canonical (or ` Kodaira\rq $)$ dimension will be considered, rather. A crucial feature of these decompositions is indeed that, in order to deal with multiple fibres of fibrations, they need to take place in the larger category of `geometric orbifolds' $(X| \Delta)$. These are `virtual ramified covers' of varieties, which `virtually eliminate' multiple fibres of fibrations. Although formally the same as the `pairs' of the LMMP (see \cite{kmm}, \cite{KM}, \cite{BCHM} and the references there), they are here fully geometric objects equipped with the usual geometric invariants of varieties, such as sheaves of (symmetric) differential forms, fundamental group, Kobayashi pseudometric, integral points, morphisms and rational maps. It is intended to expose (with some addtional topics or developments), as briefly and simply as possible, and essentially skipping the proofs, the main content of arXiv:math/0110051 and arXiv:0705.0737 respectively published in ANN. Inst. Fourier (2004), and to appear in J.Inst. Math. Jussieu.Comment: Expanded version of a talk given in May 2009 at the Schiermonnikoog Conference on birational geometry (Holland, organised by C. Faber, E. Looijenga and G. Van der Gee