Corpus ID: 236772798

Intersecting $\psi$-classes on $M_{0,w}^{\mathrm{trop}}$

@inproceedings{Hahn2021IntersectingO,
  title={Intersecting \$\psi\$-classes on \$M\_\{0,w\}^\{\mathrm\{trop\}\}\$},
  author={Marvin Anas Hahn and Shiyue Li},
  year={2021}
}
In this paper, we study the intersection products of weighted tropical ψ-classes, in arbitrary dimensions, on the moduli space of tropical weighted stable curves. We introduce the tropical Gromov–Witten multiplicity at each vertex of a given tropical curve. This concept enables us to prove that the weight of a maximal cone in an intersection of ψ-classes decomposes as the product of tropical Gromov–Witten multiplicities at all vertices of the cone’s associated tropical curves. Along the way, we… 

Figures from this paper

References

SHOWING 1-10 OF 36 REFERENCES
Intersections on tropical moduli spaces
This article explores to which extent the algebro-geometric theory of rational descendant Gromov-Witten invariants can be carried over to the tropical world. Despite the fact that the tropical
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY
We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector $w$ of weights, the moduli space of tropical $w$ -stable curves can be
Chow rings of heavy/light Hassett spaces via tropical geometry
Abstract We compute the Chow ring of an arbitrary heavy/light Hassett space M ‾ 0 , w . These spaces are moduli spaces of weighted pointed stable rational curves, where the associated weight vector w
Intersecting Psi-classes on tropical M_{0,n}
We apply the tropical intersection theory developed by L. Allermann and J. Rau to compute intersection products of tropical Psi-classes on the moduli space of rational tropical curves. We show that
New moduli spaces of pointed curves and pencils of flat connections.
It is well known that formal solutions to the Associativity Equations are the same as cyclic algebras over the homology operad $(H_*(\bar{M}_{0,n+1}))$ of the moduli spaces of $n$--pointed stable
Tropical intersection theory from toric varieties
We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary
Tropical geometry of moduli spaces of weighted stable curves
TLDR
A tropical analogue of Hassett's moduli spaces of weighted stable curves is defined and it is shown that the naive set-theoretic tropicalization map can be identified with a natural deformation retraction onto the non-Archimedean skeleton.
The diagonal of tropical matroid varieties and cycle intersections
We define an intersection product of tropical cycles on matroid varieties (via cutting out the diagonal) and show that it is well-behaved. In particular, this enables us to intersect cycles on moduli
Wall-Crossings for Hassett Descendant Potentials
This paper solves the combinatorics relating the intersection theory of $\psi$-classes of Hassett spaces to that of $\overline{\mathcal{M}}_{g,n}$. A generating function for intersection numbers of
MODULI OF WEIGHTED STABLE MAPS AND THEIR GRAVITATIONAL DESCENDANTS
We study the intersection theory on the moduli spaces of maps of $n$-pointed curves $f:(C,s_1,\dots,s_n)\to V$ which are stable with respect to the weight data $(a_1,\dots,a_n)$, $0\le a_i\le1$.
...
1
2
3
4
...