Let $overline{M}_{0,n}(G(r,V), d)$ be the coarse moduli space that parametrizes stable maps of class d from n-pointed genus 0 curves to a Grassmann variety G(r,V). We provide a recursive method for the computation of the Betti numbers and the Hodge numbers of $overline{M}_{0,n}(G(r,V), d)$ for all n and d. Our method is a generalization of Getzler and Pandharipande's work "The Betti numbers of $overline{M}_{0,n}(r,d)$". First, we reduce our problem to the calculation of the Hodge numbers of the open locus $M_{0,n}(G(r,V), d)$ corresponding to maps from smooth curves. Then, we show that those can be determined by considering a suitable compactification of the space of degree d morphisms from $mathbb{P}^1$ to G(r,V), combined with previous results on the configuration space of n distinct points on $mathbb{P}^1$.

On the cohomology of moduli spaces of stable maps to Grassmannians / Bagnarol, Massimo. - (2019 Sep 27).

On the cohomology of moduli spaces of stable maps to Grassmannians

Bagnarol, Massimo
2019

Abstract

Let $overline{M}_{0,n}(G(r,V), d)$ be the coarse moduli space that parametrizes stable maps of class d from n-pointed genus 0 curves to a Grassmann variety G(r,V). We provide a recursive method for the computation of the Betti numbers and the Hodge numbers of $overline{M}_{0,n}(G(r,V), d)$ for all n and d. Our method is a generalization of Getzler and Pandharipande's work "The Betti numbers of $overline{M}_{0,n}(r,d)$". First, we reduce our problem to the calculation of the Hodge numbers of the open locus $M_{0,n}(G(r,V), d)$ corresponding to maps from smooth curves. Then, we show that those can be determined by considering a suitable compactification of the space of degree d morphisms from $mathbb{P}^1$ to G(r,V), combined with previous results on the configuration space of n distinct points on $mathbb{P}^1$.
Perroni, Fabio
Fantechi, Barbara
Bagnarol, Massimo
File in questo prodotto:
File Dimensione Formato  
PhD_thesis_Bagnarol.pdf

accesso aperto

Tipologia: Tesi
Licenza: Non specificato
Dimensione 1.02 MB
Formato Adobe PDF
1.02 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/103198
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact