7 papers · 1 filter
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,…
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…