7 citations · 26 across the 11 of their papers we have counts for
11 papers
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 whe…
Irreducible Contact Curves via Graph Stratification
Giosuè Muratore
We prove that the moduli space of contact stable maps to of degree admits a stratification parameterized by graphs. We use it to determine the number of irr…
Effective computations of the Atiyah-Bott formula
Giosuè Muratore, Csaba Schneider
We present an implementation of the Atiyah-Bott residue formula for . We use this implementation to compute a large number of Gromov-Witten in…
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…
A Recursive Formula for Osculating Curves
Giosuè Muratore
Let be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of . We prove t…
The indeterminacy locus of the Voisin map
Giosuè Emanuele Muratore
Beauville and Donagi proved that the variety of lines of a smooth cubic fourfold is a hyperkähler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that…
Betti numbers and pseudoeffective cones in 2-Fano varieties
Giosuè Emanuele Muratore
The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) -Fano variety and c…