A geographical study of $\overline{\mathcal M}_{2}(\mathbb{P}^2,4)^{\text{main}}$

Luca Battistella; Francesca Carocci

A geographical study of $\overline{\mathcal M}_{2}(\mathbb{P}^2,4)^{\text{main}}$

Algebraic Geometry 2021-11-22 v2

Authors: Luca Battistella , Francesca Carocci

Abstract

We discuss criteria for a stable map of genus two and degree $4$ to the projective plane to be smoothable, as an application of our modular desingularisation of $\overline{\mathcal M}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$ via logarithmic geometry and Gorenstein singularities.

Keywords

moduli spaces singularity theory del pezzo surfaces

Cite

@article{arxiv.2010.15799,
  title  = {A geographical study of $\overline{\mathcal M}_{2}(\mathbb{P}^2,4)^{\text{main}}$},
  author = {Luca Battistella and Francesca Carocci},
  journal= {arXiv preprint arXiv:2010.15799},
  year   = {2021}
}

Comments

22 pages, 17 figures. Comments are welcome! v2: exposition improved thanks to the referee's comments. Final version to appear in Advances in Geometry

Related papers

View all related →