Singularities of moduli of curves with a universal root
@article{Galeotti2015SingularitiesOM, title={Singularities of moduli of curves with a universal root}, author={Mattia Galeotti}, journal={arXiv: Algebraic Geometry}, year={2015} }
In a series of recent papers, Chiodo, Farkas and Ludwig carry out a deep analysis of the singular locus of the moduli space of stable (twisted) curves with an $\ell$-torsion line bundle. They show that for $\ell\leq 6$ and $\ell\neq 5$ pluricanonical forms extend over any desingularization. This allows to compute the Kodaira dimension without desingularizing, as done by Farkas and Ludwig for $\ell=2$, and by Chiodo, Eisenbud, Farkas and Schreyer for $\ell=3$. Here we treat roots of line bundles…
3 Citations
Moduli of $G$-covers of curves: geometry and singularities
- Mathematics
- 2019
In a recent paper Chiodo and Farkas described the singular locus and the locus of non-canonical singularities of the moduli space of level curves. In this work we generalize their results to the…
Moduli of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>-covers of curves: geometry and singularities
- MathematicsAnnales de l'Institut Fourier
- 2022
References
SHOWING 1-10 OF 16 REFERENCES
Singularities of the moduli space of level curves
- Mathematics
- 2012
We describe the singular locus of the compactification of the moduli space $R_{g,l}$ of curves of genus $g$ paired with an $l$-torsion point in their Jacobian. Generalising previous work for $l\le…
Moduli of twisted spin curves
- Mathematics
- 2001
In this note we give a new, natural construction of a compactification of the stack of smooth r-spin curves, which we call the stack of stable twisted r-spin curves. This stack is identified with a…
The geometry of the moduli space of odd spin curves
- Mathematics
- 2010
The spin moduli spaceSg is the parameter space of theta characteristics (spin structures) on stable curves of genus g. It has two connected components, S g andS + g , depending on the parity of the…
On the geometry of the moduli space of spin curves
- Mathematics
- 2007
We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification \bar S_g of the moduli space S_g of spin curves, i.e., smooth curves of genus g with a theta…
Poincaré bundles for families of curves.
- Mathematics
- 1985
If X is a projective nonsingular algebraic curve and J the variety of isomorphism classes of line bundles on X of degree r, then it is a classical fact that there exists a line b ndle on J χ X which…
The Kodaira dimension of the moduli space of Prym varieties
- Mathematics
- 2008
Prym varieties provide a correspondence between the moduli spaces of curves and abelian varieties Mg and Ag−1, via the Prym map Pg : Rg → Ag−1 from the moduli space Rg parameterizing pairs [C, η],…
Compactifying the space of stable maps
- Mathematics
- 1999
We define two equivalent notions of twisted stable map from a curve to a Deligne-Mumford stack with projective moduli space, and we prove that twisted stable maps of fixed degree form a complete…
Stable twisted curves and their $r$-spin structures
- Mathematics
- 2006
L'objet, de cet, article est la notion de structure r-spin: un fibre en droites dont la puissance r-ieme est isomorphe au fibre canonique. Au-dessus du champ Mg des courbes lisses de genre g, les…
Algebraic Graph Theory
- MathematicsGraduate texts in mathematics
- 2001
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.