Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Blomme, Thomas"'
Autor:
Blomme, Thomas
We generalize a previous result by Fabricius-Bjerre from curves in $\mathbb R^2$ to curves in $\mathbb R P^2$. Applied to the case of real algebraic curves, this recovers the signed count of bitangents of quartics introduced by Larson-Vogt and proves
Externí odkaz:
http://arxiv.org/abs/2409.14727
Autor:
Blomme, Thomas, Carocci, Francesca
We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^1$-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore we prove a refinement of
Externí odkaz:
http://arxiv.org/abs/2409.09472
Autor:
Blomme, Thomas, Mével, Gurvan
Block and G\"ottsche introduced a Laurent polynomial multiplicity to count tropical curves. Itenberg and Mikhalkin then showed that this multiplicity leads to invariant counts called tropical refined invariants. Recently, Brugall\'e and Jaramillo-Pue
Externí odkaz:
http://arxiv.org/abs/2403.17474
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 topological type of the curve. From this follows that a generic real algebr
Externí odkaz:
http://arxiv.org/abs/2402.03993
Autor:
Blomme, Thomas
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 point insertions using a floor diagram algorithm. Using the latter, we ar
Externí odkaz:
http://arxiv.org/abs/2401.01627
Autor:
Blomme, Thomas, Schleis, Victoria
We consider the enumeration of tropical curves in M\"obius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we prove regu
Externí odkaz:
http://arxiv.org/abs/2309.06995
Autor:
Blomme, Thomas, Markwig, Hannah
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 to compute tropically: for instance, there are (generalized) lattice pa
Externí odkaz:
http://arxiv.org/abs/2212.06603
Autor:
Blomme, Thomas
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 diagram algorithm similar to the floor diagram algorithm used in tori
Externí odkaz:
http://arxiv.org/abs/2205.07684
Autor:
Blomme, Thomas
In this paper, second installment in a series of three, we give a correspondence theorem to relate the count of genus $g$ curves in a fixed linear system in an abelian surface to a tropical count. To do this, we relate the linear system defined by a
Externí odkaz:
http://arxiv.org/abs/2202.09768
Autor:
Blomme, Thomas
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 consider the enumeration of genus $g$ curves of fixed degree passing through
Externí odkaz:
http://arxiv.org/abs/2202.07250