6 citations · 20 across the 19 of their papers we have counts for
21 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…
Refined invariants for Abelian surfaces: between polynomiality and modularity
Thomas Blomme, Gurvan Mével
Tropical refined invariants for toric surfaces, introduced Block and G{ö}ttsche, are obtained couting tropical curves with a Laurent polynomial multiplicity. Brugall{é} and Jaramil…
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…
A short proof of the multiple cover formula for point insertions
Thomas Blomme
A few years ago, G. Oberdieck conjectured a multiple cover fomula that determines the number of curves of fixed genus and degree passing through a configuration of points in an abe…
On the double tangent of projective closed curves
Thomas Blomme
We generalize a previous result by Fabricius-Bjerre from curves in to curves in . Applied to the case of real algebraic curves, this recovers the signe…
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…
Asymptotic computations of tropical refined invariants in genus 0 and 1
Thomas Blomme, Gurvan Mével
Block and Göttsche introduced a Laurent polynomial multiplicity to count tropical curves. Itenberg and Mikhalkin then showed that this multiplicity leads to invariant counts called…
Bitangents of real algebraic curves: signed count and constructions
Thomas Blomme, Erwan Brugallé, Cristhian Garay
We study real bitangents of real algebraic plane curves from two perspectives. We first show that there exists a signed count of such bitangents that only depends on the real topol…
Gromov-Witten Invariants of Bielliptic Surfaces
Thomas Blomme
Bielliptic surfaces appear as quotient of a product of two elliptic curves and were classified by Bagnera-Franchis. We give a concrete way of computing their GW-invariants with poi…
Tropical Möbius strips and ruled surfaces
Thomas Blomme, Victoria Schleis
We consider the enumeration of tropical curves in Möbius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces ove…
Tropical descendant invariants with line constraints
Thomas Blomme, Hannah Markwig
Via correspondence theorems, rational log Gromov--Witten invariants of the plane can be computed in terms of tropical geometry. For many cases, there exists a range of algorithms t…
Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas
Thomas Blomme
This paper is the third installment in a series of papers devoted to the computation of enumerative invariants of abelian surfaces through the tropical approach. We develop a pearl…
Tropical curves in abelian surfaces II: enumeration of curves in linear systems
Thomas Blomme
In this paper, second installment in a series of three, we give a correspondence theorem to relate the count of genus curves in a fixed linear system in an abelian surface to a…
Tropical curves in abelian surfaces I: enumeration of curves passing through points
Thomas Blomme
This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we conside…
Floor diagrams and enumerative invariants of line bundles over an elliptic curve
Thomas Blomme
We use the tropical geometry approach to compute absolute and relative Gromov-Witten invariants of complex surfaces which are $\CC P^1$-bundles over an elliptic curve. We also show…
Refined count of real oriented rational curves
Thomas Blomme
We introduce a \textit{quantum index} for oriented real curves inside toric varieties. This quantum index is related to the computation of the area of the amoeba of the curve for s…
Refined count for rational tropical curves in arbitrary dimension
Thomas Blomme
In this paper we introduce a refined multiplicity for rational tropical curves in arbitrary dimension, which generalizes the refined multiplicity introduced by F. Block and L. Gött…
Computation of refined toric invariants II
Thomas Blomme
In 2015, G.~Mikhalkin introduced a refined count for real rational curves in toric surfaces. The counted curves have to pass through some real and complex points located on the tor…
A Tropical Computation of Refined Toric Invariants
Thomas Blomme
In arXiv:1505.04338(4), G. Mikhalkin introduced a refined count for the real rational curves in a toric surface which pass through certain conjugation invariant set of points on th…
A Caporaso-Harris type Formula for relative refined invariants
Thomas Blomme
G. Mikhalkin introduced a refined count for real rational curves in a toric surface which pass through some points on the toric boundary of the surface. The refinement is provided…