Results 1 to 10 of about 2,693,089 (183)

Arithmetic geometry of algebraic curves and their moduli space [PDF]

arXiv, 2014
We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories to the arithmetic of the moduli space of algebraic curves, especially to automorphic forms on this space.
Takashi Ichikawa
openalex   +3 more sources

Algebraic structures on the topology of moduli spaces of curves and maps [PDF]

arXiv, 2008
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
Y. P. Lee, Ravi Vakil
openalex   +3 more sources

Cohomology of Moduli Stacks of Principal $\Bbb C^*$-Bundles Over Nodal Algebraic Curves [PDF]

arXiv
We study moduli stacks of principal $\Bbb C^*$-bundles over nodal complex algebraic curves and determine their rational cohomology algebras in terms of Chern classes.
Abel Castorena, Frank Neumann
openalex   +2 more sources

A moduli stack of tropical curves [PDF]

Forum of Mathematics, Sigma 8 (2020) e23, 2017
We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show that it is representable by a geometric stack over the category of rational polyhedral cones.
arxiv   +1 more source

Moduli Spaces of Rational Graphically Stable Curves [PDF]

arXiv, 2022
We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterize when the tropical compactification of the moduli space agrees with the theory of geometric tropicalization. The characterization statement occurs only when the graph is complete multipartite.
arxiv  

Stable cohomology of moduli spaces of hyperelliptic curves on Hirzebruch surfaces [PDF]

arXiv, 2023
We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed non-embedded hyperelliptic curves.
arxiv  

Enriched spin curves on stable curves with two components [PDF]

arXiv, 2008
L. Maino constructed a moduli space for enriched stable curves, by blowing-up the moduli space of Deligne-Mumford stable curves. We introduce enriched spin curves, showing that a parameter space for these objects is obtained by blowing-up the moduli space of spin curves.
arxiv  

Moduli of Legendrian Curves [PDF]

arXiv, 2009
We construct the generic component of the moduli space of the germs of Legendrian curves with generic plane projection topologicaly equivalent to a curve y^n = x^m, (n,m)=1.
arxiv  

Rationality of the Moduli Variety of Curves of Genus 3 [PDF]

arXiv, 1994
We prove rationality of the moduli variety of curves of genus 3.
arxiv  

Lectures on tropical curves and their moduli spaces [PDF]

arXiv, 2016
These are notes for a series of five lectures on "Moduli and degenerations of algebraic curves via tropical geometry" delivered at the CIMPA-CIMAT-ICTP School on Moduli of Curves, February 29-March 4, 2016 in Guanajuato, Mexico.
arxiv