50 research outputs found
Boundary and Eisenstein Cohomology of
In this article, several cohomology spaces associated to the arithmetic
groups and with
coefficients in any highest weight representation have
been computed, where denotes their highest weight. Consequently, we
obtain detailed information of their Eisenstein cohomology with coefficients in
. When is not self dual, the
Eisenstein cohomology coincides with the cohomology of the underlying
arithmetic group with coefficients in . In particular, for
such a large class of representations we can explicitly describe the cohomology
of these two arithmetic groups. We accomplish this by studying the cohomology
of the boundary of the Borel-Serre compactification and their Euler
characteristic with coefficients in . At the end, we
employ our study to discuss the existence of ghost classes.Comment: 42 Pages, 1 Figure, 9 Tables, To Appear in Math. Annale
Birational properties of some moduli spaces related to tetragonal curves of genus 7
Let M_{7,n} be the (coarse) moduli space of smooth curves of genus 7 with n
marked points defined over the complex field. We denote by M^1_{7,n;4} the
locus of points inside M_{7,n} representing curves carrying a g^1_4. It is
classically known that M^1_{7,n;4} is irreducible of dimension 17+n. We prove
in this paper that M^1_{7,n;4} is rational for 0<= n <= 11.Comment: 20 pages; in the second version we replaced the previous Lemma 4.3 by
Lemma 4.5, and fixed the proof of the rationality of the moduli space of
unpointed tetragonal genus 7 curves in section 4. Hans-Christian von Bothmer
as further author adde