Karl Christ

Welcome to my math page!

I am an assistant professor at the University of Turin. Before that, I held postdoc positions at UT Austin, Leibniz University Hannover and Ben-Gurion University, Be'er Sheva.

I did my PhD at Roma Tre University with Lucia Caporaso.

My research area lies in algebraic and tropical geometry. So far, my work has been centered around these topics: compactified Jacobians, Mumford models, Severi varieties of toric surfaces and the rank of divisors on nodal and tropical curves.

Contact

email: karlchrist (gmail.com)

Via Carlo Alberto, 10

10123 Torino (Italy)

with Xiang He and Ilya Tyomkin: The irreducibility of Hurwitz spaces and Severi varieties on toric surfaces; arXiv: 2501.16238 (2025).
with Myrla Barbosa and Margarida Melo: Clifford representatives via the uniform algebraic rank, J. London Math. Soc., 111: e70193 (2025); arXiv: 2406.03987.
with Xiang He and Ilya Tyomkin: Balancing properties of tropical moduli maps; arXiv: 2403.15686 (2024).
Special divisors in special divisor classes on graphs, Rend. Circ. Mat. Palermo, II. Ser 74, 169 (2025); arXiv: 2312.13207.
with Qixiao Ma: Bounding the number of graph refinements for Brill-Noether existence; arXiv: 2304.07405 (2023).
A Clifford inequality for semistable curves, Mathematische Zeitschrift 303, 15 (2023); arXiv: 2204.08234.
with Xiang He and Ilya Tyomkin: Degeneration of curves on some polarized toric surfaces, Journal für die reine und angewandte Mathematik, no. 787, pp. 197-240 (2022); arXiv: 2012.06766.
with Xiang He and Ilya Tyomkin: On the Severi problem in arbitrary characteristic, Publ. Math. IHÉS 137, pp. 1 - 45 (2023); arXiv: 2005.04134.
On the rank of general linear series on stable curves, Mathematische Annalen 388, pp. 2217–2240 (2024); arXiv: 2005.12817.
with Sam Payne and Tif Shen: Compactified Jacobians as Mumford models, Transactions of the AMS 376, pp. 4605 - 4630 (2023); arXiv: 1912.03653.
with Lucia Caporaso: Combinatorics of compactified universal Jacobians, Advances in Mathematics, 346, pp. 1091 - 1136 (2019); arXiv: 1801.04098.
Orientations, break divisors and compactified Jacobians (2018), PhD thesis.

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