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Now showing items 1-10 of 11

#### 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 ...

#### Twistor spaces with a pencil of fundamental divisors

(Documenta Mathematica, 1999)

In this paper simply connected twistor spaces Z containing a pencil of fundamental divisors are studied. The Riemannian base for such spaces is diffeomorphic to the connected sum nCP2 . We obtain for n 5 a complete ...

#### Analytic moduli spaces of simple sheaves on families of integral curves (Pre-print version)

(Wiley, 2013)

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, ...

#### 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

(Springer, 2006)

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 ...

#### Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes

(American Mathematical Society, 1999)

We prove the existence of twistor spaces of algebraic dimension
two over the connected sum of four complex projective planes 4CP2. These are
the rst examples of twistor spaces of algebraic dimension two over a ...

#### Algebraic dimension of twistor spaces whose fundamental system is a pencil (pre-published version)

(London Mathematical Society, 2017)

We show that the algebraic dimension of a twistor space over nℂℙ2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half‐anti‐canonical bundle, which is available on any twistor ...

#### The Belavin-Drinfeld theorem on non-degenerate solutions of the classical Yang-Baxter equation

(IOP Publishing, 2010)

We give a coordinate free proof of Belavin and Drinfeld's Theorem about the classi cation of non-degenerate solutions of the classical Yang-Baxter equation. The equivalence of different characterisations of non-degeneracy ...

#### Moishezon twistor spaces without effective divisors of degree one (pre-published version)

(Universität Kaiserslautern, 1995)

We study simply connected compact twistor spaces Z of positive type. Assuming that the fundamental linear system j \Gamma 1 2 Kj is at least a pencil, we prove the following theorem: the existence of an irreducible curve ...

#### Ireland's participation in the 50th international mathematical olympiad

(Irish Mathematical Society, 2009)

The 50th International Mathematical Olympiad (IMO) took place in Bremen (Germany) from 12th July until 22nd July 2009. With 565 participants (59 of whom were girls) from 104 countries, this was the IMO with the largest ...