11 citations · 25 across the 13 of their papers we have counts for
15 papers
A correlated refinement of the double double ramification cycle
Thomas Blomme, Francesca Carocci, Ajith Urundolil Kumaran
Given a family of semi-stable curves together with two degree 0 line bundles, the double double ramification cycle measures the locus where both line bundles are trivial on the fib…
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…
Multiple cover formulas for abelian surfaces via correlated invariants
Thomas Blomme, Francesca Carocci
We prove the multiple cover formula conjecture for abelian surfaces for a large class of insertions, including all stationary invariants. The proof uses the reduced degeneration fo…
Correlated double ramification cycle formula
Thomas Blomme, Francesca Carocci
We prove a refinement of Pixton's formula for the double ramification cycle with target variety which takes into account the correlator of a rubber map previously introduced by the…
Chow theory of toric variety bundles
Francesca Carocci, Leonid Monin, Navid Nabijou
We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as…
Correlated Gromov-Witten Invariants
Thomas Blomme, Francesca Carocci
We introduce a geometric refinement of Gromov-Witten invariants for -bundles relative to the natural fiberwise boundary structure. We call these refined invariant corr…
Tropical expansions and toric variety bundles
Francesca Carocci, Navid Nabijou
A tropical expansion is a degeneration of a toroidal embedding, induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admit…
BPS invariants from -adic integrals
Francesca Carocci, Giulio Orecchia, Dimitri Wyss
We define -adic BPS or BPS-invariants for moduli spaces of 1-dimensional sheaves on del Pezzo surfaces by means of integration over a non-archimedean local field $F…
Rubber tori in the boundary of expanded stable maps
Francesca Carocci, Navid Nabijou
We investigate torus actions on logarithmic expansions in the context of enumerative geometry. Our main result is an intrinsic and coordinate-free description of the higher-rank ru…
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…
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…
Endomorphisms of Koszul complexes: formality and application to deformation theory
Francesca Carocci, Marco Manetti
We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative -algebra and we prove that it is homoto…
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…
Homological projective duality for linear systems with base locus
Francesca Carocci, Zak Turcinovic
We show how blowing up varieties in base loci of linear systems gives a procedure for creating new homological projective duals from old. Starting with a HP dual pair and smo…