We state and prove a long-elusive relation between genus-one Gromov-Witten of a complete intersection and twisted Gromov-Witten invariants of the ambient projective space. As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component M 0 1,k(P , d) of the moduli space of stable genus-one holomorphic maps into P have a well-defined eu...

The image of the principal minor map for n×n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n = 4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in P15. The latter...

Carrying further work of T.A. Crawford, we show that each component of the space of harmonic maps from the 2-sphere to complex projective 2-space of degree d and energy 4πE is a smooth closed submanifold of the space of all C j maps (j ≥ 2). We achieve this by showing that the Gauss transform which relates them to spaces of holomorphic maps of given degree and ramification index is smooth and h...

In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational invariants a transcendence basis in terms of Schofield’s determinantal semi-invariants. We also show that the moduli space of modules over a regular irreducib...

We develop a formula (Theorem 5.1) which allows to compute top Chern classes of vector bundles on the vanishing locus V (s) of a section of this bundle. This formula particularly applies in the case when V (s) is the union of locally complete intersections giving the individual contribution of each component and their mutual intersections. We conclude with applications to the enumeration of rat...

This paper describes the implementation of behaviour for real-time visual servoing on a mobile robot. The behaviour is a component of a multi-robot cleaning system developed in the context of our investigation into architectures for cooperative systems. An important feature for support of cooperation is the awareness of one robot by another, which this behaviour realises. Robust feature trackin...

In a 6-month longitudinal design, the authors examined the links between neediness and increases in depressive symptoms in women. Neediness was assessed with the self-report Depressive Experiences Questionnaire (DEQ), supplemented by a projective measure that assessed an important component of dependency, oral dependency, on the Rorschach. Results indicate that neediness correlated significantl...

We give two applications of our earlier work[4]. We compute the p-adic cohomology of certain exponential sums on An involving a polynomial whose homogeneous component of highest degree defines a projective hypersurface with at worst weighted homogeneous isolated singularities. This study was motivated by recent work of Garćıa[9]. We also compute the p-adic cohomology of certain exponential sums...