Now showing items 1-10 of 15
Solving cubic equations in two variables
(Irish Mathematical Society, 2007)
After recalling a geometric construction of all Pythagorean triples of integers, the same idea is applied to find rational solutions of cubic equations in two variables. This leads to the definition of the Mordell-Weil ...
Torelli theorem for the Deligne-Hitchin moduli space (Pre-published version)
(Springer Verlag, 2009)
Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let M DH (X) denote the corresponding SL(r,C) Deligne–Hitchin moduli space. We prove that the complex analytic ...
Homological algebra with locally compact abelian groups (Pre-published Version)
In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We deﬁne a well-behaved derived Hom-complex ...
Derived categories of irreducible projective curves of arithmetic genus one
(Cambridge Journals, 2006)
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures ...
On a relative Fourier-Mukai transform on genus one fibrations
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a ...
Rationality and Poincaré families for vector bundles with extra structure on a curve (Pre-published version)
(Oxford University Press, 2007)
Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. ...
The Boden-Hu conjecture holds precisely up to rank eight (Pre-published version)
(Springer Verlag, 2004)
Stability of Arakelov bundles and tensor products without global sections
(Documenta Mathematica, 2003)
This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there is a bundle F such that E⊗F has at least ...
Minimizing oblique errors for robust estimating
(Irish Mathematical Society, 2008)
The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show ...
On semistable vector bundles over curves (Pre-published version)
Let X be a geometrically irreducible smooth projective curve de ned over a eld k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X; F E) = 0 for i = 0; ...