# Euler characteristic of quiver Grassmannians and Ringel-Hall algebras of string algebras

Nicolas Poettering

Number | 48 |
---|---|

Author | Nicolas Poettering |

Project | C01 |

Year | 2010 |

We compute the Euler characteristics of quiver Grassmannians and quiver flag
varieties of tree and band modules and prove their positivity. This generalizes
some results by G.C. Irelli [arXiv:0910.2592].

As an application we consider the Ringel-Hall algebra C(A) of some string
algebras A and compute in combinatorial terms the products of arbitrary
functions in C(A).