27 research outputs found
On the Euler characteristic of Kronecker moduli spaces
Combining the MPS degeneration formula for the Poincar\'e polynomial of
moduli spaces of stable quiver representations and localization theory, it
turns that the determination of the Euler characteristic of these moduli spaces
reduces to a combinatorial problem of counting certain trees. We use this fact
in order to obtain an upper bound for the Euler characteristic in the case of
the Kronecker quiver. We also derive a formula for the Euler characteristic of
some of the moduli spaces appearing in the MPS degeneration formula.Comment: 15 page
On the recursive construction of indecomposable quiver representations
For a fixed root of a quiver, it is a very hard problem to construct all or
even only one indecomposable representation with this root as dimension vector.
We investigate two methods which can be used for this purpose. In both cases we
get an embedding of the category of representations of a new quiver into the
category of representations of the original one which increases dimension
vectors. Thus it can be used to construct indecomposable representations of the
original quiver recursively. Actually, it turns out that there is a huge class
of representations which can be constructed using these methods.Comment: 20 pages, final versio