Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/0505012

Gromov-Witten invariants of P^2-stacks

Charles Cadman
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Gromov-Witten theory of Deligne-Mumford stacks is a recent development, and hardly any computations have been done beyond 3-point genus 0 invariants. This paper provides explicit recursions which, together with some invariants computed by hand, determine all genus 0 invariants of the stack P^2_{D,2}. Here D is a smooth plane curve and P^2_{D,2} is locally isomorphic to the stack quotient [U/(Z/(2))], where U -> V \subset P^2 is a double cover branched along D \cap V. The introduction discusses an enumerative application of these invariants.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Charles Cadman. 2006-09-08. Gromov-Witten invariants of P^2-stacks. https://arxiv.org/abs/math/0505012

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Geometric Detection and Finiteness of Log Crystalline Local Systems

We prove a geometric detection theorem for log crystalline local systems in the smooth proper setting with a normal crossings boundary. The associated special-fiber log $F$-isocrystal detects geometric absolute irreducibility and, modulo constant rank-one twists, determines the pullback to the geometric generic fiber. The main ingredient is a determinant argument combining a finite-order rank-one reduction, logarithmic period comparison, and the Plücker embedding. As an application, using Abe--Esnault's finiteness theorem and finiteness of stable lattices, we prove finiteness, up to geometrically constant rank-one twists, of geometrically absolutely irreducible log crystalline local systems of fixed rank. Coefficients may lie in any fixed finite extension of $\mathbb Q_p$, and no bound on the Hodge--Tate weights is imposed.

math.AG↗
arXiv2026

Betti Numbers of Odd Biisotropic Symplectic Grassmannians

We compute the singular cohomology groups of odd biisotropic symplectic Grassmannians $\operatorname{S_2Gr}(k, 2n+1)$ by presenting an explicit dimension-preserving combinatorial bijection between the Bialynicki-Birula cells in $\operatorname{S_2Gr}(k, 2n+1)$ and the Schubert cells in $\operatorname{Gr}(k, 2n+2-k)$.

math.AG↗
arXiv2026

Motivic $C_p$-power operations in $\mathrm{MGL}$

In this paper, we give a new proof of the Hopkins-Morel-Hoyois theorem for fields $k$ of characteristic unequal to $p$ containing all primitive $p$-power roots of unity for a fixed prime $p$. This new proof follows Quillen's proof for the structure of the homotopy groups of $\mathrm{MU}$ which utilizes topological power operations. To this end we define a motivic analog of the Steenrod power operations, using the theory of normed motivic spectra as developed by Bachmann--Hoyois and their application for the definition of motivic colimits as developed by Bachmann-Elmanto-Heller.

math.AG↗