Christoph Goldner

collaborators

4 papers

math.AG2020

Counting tropical rational space curves with cross-ratio constraints

Christoph Goldner

This is a follow-up paper of arXiv:1805.00115, where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable corres…

math.AG2020

Generalizing tropical Kontsevich's formula to multiple cross-ratios

Christoph Goldner

Kontsevich's formula is a recursion that calculates the number of rational degree $d$ curves in $P_{C}^{2}$ passing through $3 d - 1$ general positioned points. Kontse…

math.AG2018

Counts of (tropical) curves in $E \times P^{1}$ and Feynman integrals

Janko Böhm, Christoph Goldner, Hannah Markwig

We study generating series of Gromov-Witten invariants of $E \times P^{1}$ and their tropical counterparts. Using tropical degeneration and floor diagram techniques, we can ex…

math.AG2018

Counting tropical rational curves with cross-ratio constraints

Christoph Goldner

We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is arXiv:1…

Counting tropical rational space curves with cross-ratio constraints

Generalizing tropical Kontsevich's formula to multiple cross-ratios

Counts of (tropical) curves in E×P1 and Feynman integrals

Counting tropical rational curves with cross-ratio constraints

Counts of (tropical) curves in $E \times P^{1}$ and Feynman integrals