138 research outputs found
A Vanishing Result for the Universal Bundle on a Toric Quiver Variety
Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine
moduli space of stable thin sincere representations of Q with respect to the
canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute
the endomorphism algebra of the universal bundle U. Moreover, we obtain a
necessary and sufficient condition for when this algebra is isomorphic to the
path algebra kQ of the quiver Q. If so, then the bounded derived category of
finitely generated right kQ-modules is embedded into that of coherent sheaves
on M.Comment: 13 pages with a couple of small figures LaTeX 2.0
Quivers and moduli spaces of pointed curves of genus zero
We construct moduli spaces of representations of quivers over arbitrary
schemes and show how moduli spaces of pointed curves of genus zero like the
Grothendieck-Knudsen moduli spaces and the Losev-Manin
moduli spaces can be interpreted as inverse limits of moduli
spaces of representations of certain bipartite quivers. We also investigate the
case of more general Hassett moduli spaces of weighted
pointed stable curves of genus zero.Comment: 41 page
Tilting Bundles on Rational Surfaces and Quasi-Hereditary Algebras
Let be any rational surface. We construct a tilting bundle on .
Moreover, we can choose in such way that its endomorphism algebra is
quasi-hereditary. In particular, the bounded derived category of coherent
sheaves on is equivalent to the bounded derived category of finitely
generated modules over a finite dimensional quasi-hereditary algebra . The
construction starts with a full exceptional sequence of line bundles on and
uses universal extensions. If is any smooth projective variety with a full
exceptional sequence of coherent sheaves (or vector bundles, or even complexes
of coherent sheaves) with all groups \mExt^q for vanishing, then
also admits a tilting sheaf (tilting bundle, or tilting complex,
respectively) obtained as a universal extension of this exceptional sequence.Comment: 15 page
On the complement of the dense orbit for a quiver of type \Aa
Let \Aa_t be the directed quiver of type \Aa with vertices. For each
dimension vector there is a dense orbit in the corresponding representation
space. The principal aim of this note is to use just rank conditions to define
the irreducible components in the complement of the dense orbit. Then we
compare this result with already existing ones by Knight and Zelevinsky, and by
Ringel. Moreover, we compare with the fan associated to the quiver \Aa and
derive a new formula for the number of orbits using nilpotent classes. In the
complement of the dense orbit we determine the irreducible components and their
codimension. Finally, we consider several particular examples.Comment: 16 pages, 9 figure
On the complement of the Richardson orbit
We consider parabolic subgroups of a general algebraic group over an
algebraically closed field whose Levi part has exactly factors. By a
classical theorem of Richardson, the nilradical of a parabolic subgroup has
an open dense -orbit. In the complement to this dense orbit, there are
infinitely many orbits as soon as the number of factors in the Levi part is
. In this paper, we describe the irreducible components of the
complement. In particular, we show that there are at most irreducible
components.Comment: 15 page
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