Zobrazeno 1 - 10
of 188
pro vyhledávání: '"Markwig, Hannah"'
We define a new class of enumerative invariants called $k$-leaky double Hurwitz descendants, generalizing both descendant integrals of double ramification cycles and the $k$-leaky double Hurwitz numbers introduced in previous work of Cavalieri, Markw
Externí odkaz:
http://arxiv.org/abs/2404.10168
Autor:
Hahn, Marvin Anas, Markwig, Hannah
Hurwitz numbers enumerate branched morphisms between Riemann surfaces. For a fixed elliptic target, Hurwitz numbers are intimately related to mirror symmetry following work of Dijkgraaf. In recent work of Chapuy and Dolega a new variant of Hurwitz nu
Externí odkaz:
http://arxiv.org/abs/2403.00333
We present an enhanced algorithm for exploring mirror symmetry for elliptic curves through the correspondence of algebraic and tropical geometry, focusing on Gromov-Witten invariants of elliptic curves and, in particular, Hurwitz numbers. We present
Externí odkaz:
http://arxiv.org/abs/2311.11381
We provide explicit faithful re-embeddings for all hyperelliptic curves of genus at most three and an algorithmic way to construct them. Both in the faithful tropicalization algorithm and the proofs of correctness, we showcase OSCAR-methods for commu
Externí odkaz:
http://arxiv.org/abs/2310.02947
Recently, the first and third author proved a correspondence theorem which recovers the Levine-Welschinger invariants of toric del Pezzo surfaces as a count of tropical curves weighted with arithmetic multiplicities. In this paper, we study propertie
Externí odkaz:
http://arxiv.org/abs/2309.12586
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 1308-1312
We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one coming from the closures of connected components of the avoidance locus and another coming from tropical geometry. When both are defined, we use the Tarski prin
Externí odkaz:
http://arxiv.org/abs/2303.07837
Counting tropical curves in $\mathbb{P}^1\times\mathbb{P}^1$: computation & polynomiality properties
Counts of curves in $\mathbb{P}^1\times\mathbb{P}^1$ with fixed contact order with the toric boundary and satisfying point conditions can be determined with tropical methods by Mikhalkin. If we require that our curves intersect the zero- and infinity
Externí odkaz:
http://arxiv.org/abs/2212.11097
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:
Hahn, Marvin Anas, Markwig, Hannah
Hurwitz numbers count covers of curves satisfying fixed ramification data. Via monodromy representation, this counting problem can be transformed to a problem of counting factorizations in the symmetric group. This and other beautiful connections mak
Externí odkaz:
http://arxiv.org/abs/2210.00595
We explore extensions of tropical methods to arithmetic enumerative problems such as $\mathbb{A}^1$-enumeration with values in the Grothendieck-Witt ring, and rationality over Henselian valued fields, using bitangents to plane quartics as a test case
Externí odkaz:
http://arxiv.org/abs/2207.01305