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Instanton bundles on Fano threefolds

Alexander Kuznetsov (2012)

Open Mathematics

We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.

Instanton sheaves on complex projective spaces.

Marcos Jardim (2006)

Collectanea Mathematica

We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of moduli spaces of instanton sheaves.

Integral models for moduli spaces of G -torsors

Martin Olsson (2012)

Annales de l’institut Fourier

Given a finite tame group scheme G , we construct compactifications of moduli spaces of G -torsors on algebraic varieties, based on a higher-dimensional version of the theory of twisted stable maps to classifying stacks.

Intersecting a plane with algebraic subgroups of multiplicative groups

Enrico Bombieri, David Masser, Umberto Zannier (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Consider an arbitrary algebraic curve defined over the field of all algebraic numbers and sitting in a multiplicative commutative algebraic group. In an earlier article from 1999 bearing almost the same title, we studied the intersection of the curve and the union of all algebraic subgroups of some fixed codimension. With codimension one the resulting set has bounded height properties, and with codimension two it has finiteness properties. The main aim of the present work is to make a start on such...

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