Search results for "algebraic curves"
showing 4 items of 14 documents
The Tautological Ring of Spin Moduli Spaces
2009
We introduce the notion of tautological ring for the moduli space of spin curves. Moreover, we study some relations among tautological classes which are motivated by physics. Finally, we show that the Chow rings of these moduli spaces are tautological in low genus.
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
2014
Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good family for $\mathcal{M}_{n,2n+2}$ is Zariski dense in the corresponding symplectic or orthogonal group if $n\geq 3$. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever $n\geq 3$. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of $m$ ordered points in $\mathbb{P}^n$ is shown to be large once it is not…
Some Moduli and Constants Related to Metric Fixed Point Theory
2001
Indeed, there are a lot of quantitative descriptions of geometrical properties of Banach spaces. The most common way for creating these descriptions, is to define a real function (a “modulus” depending on the Banach space under consideration, and from this define a suitable constant or coefficient closely related to this function. The moduli and/or the constants are attempts to get a better understanding about two things: The shape of the unit ball of a space, and The hidden relations between weak and strong convergence of sequences.
Euler Characteristics of Moduli Spaces of Curves
2005
Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford compactification of ${mathcal M}_g^n$. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of ${\bar {\mathcal M}}_g^n$ for any g and n such that n>2-2g.