11 citations · 54 across the 12 of their papers we have counts for
14 papers
Vector bundles on Olsson fans
Luca Battistella, Francesca Carocci, Jonathan Wise
Artin fans are algebro-geometric incarnations of cone complexes. We study weakly convex Olsson fans, generalising Artin fans in two ways: first, they admit lineality spaces, thus i…
Euler characteristics of higher rank double ramification loci in genus one
Luca Battistella, Navid Nabijou
Double ramification loci parametrise marked curves where a weighted sum of the markings is linearly trivial; higher-rank loci are obtained by imposing several such conditions simul…
Logarithmic negative tangency and root stacks
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov…
Hyperelliptic Gorenstein curves and logarithmic differentials
Luca Battistella, Sebastian Bozlee
We produce a flexible tool for contracting subcurves of logarithmic hyperelliptic curves, which is local around the subcurve and commutes with arbitrary base-change. As an applicat…
Buildings, valuated matroids, and tropical linear spaces
Luca Battistella, Kevin Kuehn, Arne Kuhrs +2
Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of parametrizes flags of subspaces/lattices in or,…
Gromov-Witten theory via roots and logarithms
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
Orbifold and logarithmic structures provide independent routes to the virtual enumeration of curves with tangency orders for a simple normal crossings pair . The theories do…
The local-orbifold correspondence for simple normal crossings pairs
Luca Battistella, Navid Nabijou, Hsian-Hua Tseng +1
For a smooth projective variety and a simple normal crossings divisor, we establish a precise cycle-level correspondence between the genus zero local Gromov-…
A geographical study of
Luca Battistella, Francesca Carocci
We discuss criteria for a stable map of genus two and degree to the projective plane to be smoothable, as an application of our modular desingularisation of $\overline{\mathcal…
A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
Luca Battistella, Francesca Carocci
We construct a modular desingularisation of . The geometry of Gorenstein singularities of genus two leads us to consider…
Curve counting in genus one: elliptic singularities & relative geometry
Luca Battistella, Navid Nabijou, Dhruv Ranganathan
We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Wi…
Modular compactifications of with Gorenstein singularities
Luca Battistella
We study the geometry of Gorenstein curve singularities of genus two, and of their stable limits. These singularities come in two families, corresponding to either Weierstrass or c…
Virtual classes for the working mathematician
Luca Battistella, Francesca Carocci, Cristina Manolache
This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual…
Reduced invariants from cuspidal maps
Luca Battistella, Francesca Carocci, Cristina Manolache
We consider genus 1 enumerative invariants arising from the Smyth-Viscardi moduli space of stable maps from curves with nodes and cusps. We prove that these invariants are equal to…
Relative quasimaps and mirror formulae
Luca Battistella, Navid Nabijou
We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When is a smooth toric variety and is a smooth very ample hypersurface in…