7 papers · 1 filter
Computations in equivariant Gromov-Witten theory of GKM spaces
Daniel Holmes, Giosuè Muratore
We study equivariant Gromov-Witten invariants and quantum cohomology in GKM theory. Building on the localization formula, we prove that the resulting expression is independent of t…
Quadratic counts of highly tangent lines to hypersurfaces
Stephen McKean, Giosuè Muratore, Wern Juin Gabriel Ong
We give two geometric interpretations for the local type of a line that is highly tangent to a hypersurface in a single point. One interpretation is phrased in terms of the Wronski…
Relative Gromov-Witten and maximal contact conics
Giosuè Muratore
We discuss some properties of the relative Gromov--Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley's sextactic c…
An arithmetic count of osculating lines
Giosuè Muratore
We say that a line in is osculating to a hypersurface if they meet with contact order . When , it is known that through a fixed point of $…
Computations of Gromov-Witten invariants of toric varieties
Giosuè Muratore
We present the Julia package ToricAtiyahBott.jl, providing an easy way to perform the Atiyah-Bott formula on the moduli space of genus stable maps wh…
Enumeration of rational contact curves via torus actions
Giosuè Muratore
We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerat…