Luca Schaffler - Research

Preprints:

• An explicit wall crossing for the moduli space of hyperplane arrangements (with P. Gallardo), (2024). Submitted. (arXiv)
• Simplices osculating rational normal curves (with A. Caminata, E. Carlini), (2024). Submitted. (arXiv)
• Compact moduli of Enriques surfaces with a numerical polarization of degree 2 (with V. Alexeev, P. Engel, D. Z. Garza), (2023). Submitted. (arXiv)

Publications:

1. The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces (with R. Moschetti, F. Rota), (2023). To appear in Documenta Mathematica. (arXiv)
2. Determinantal varieties from point configurations on hypersurfaces (with A. Caminata, H.-B. Moon). International Mathematics Research Notices (2023), no. 22, 19743–19772. (published version) (arXiv)
3. Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces (with P. Gallardo, G. Pearlstein, Z. Zhang). Mathematische Nachrichten 297 (2024), no. 2, 595–628. (published version) (arXiv)
4. Gaussian likelihood geometry of projective varieties (with S. Di Rocco, L. Gustafsson). SIAM Journal on Applied Algebra and Geometry 8 (2024), no. 1, 89–113. (published version) (arXiv)
5. A computational view on the non-degeneracy invariant for Enriques surfaces (with R. Moschetti, F. Rota). Experimental Mathematics. Published online: 29 August 2022. (published version) (arXiv) (code)
6. Families of pointed toric varieties and degenerations (with S. Di Rocco). Mathematische Zeitschrift 301 (2022), no. 4, 4119–4139. (published version) (arXiv)
7. Compactifications of moduli of points and lines in the projective plane (with J. Tevelev). International Mathematics Research Notices (2022), no. 21, 17000–17078. (published version) (arXiv)
8. Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces (with P. Gallardo, M. Kerr). Advances in Mathematics 381 (2021). (published version) (arXiv)
9. Point configurations, phylogenetic trees, and dissimilarity vectors (with A. Caminata, N. Giansiracusa, H.-B. Moon). Proceedings of the National Academy of Sciences of the United States of America (PNAS) March 23, 2021 118 (12). (published version) (arXiv)
10. Decomposition of Lagrangian classes on K3 surfaces (with K.-W. Lai, Y.-S. Lin). Mathematical Research Letters 28 (2021), no. 6, 1739–1763. (published version) (arXiv)
11. A Pascal's theorem for rational normal curves (with A. Caminata). Bulletin of the London Mathematical Society 53 (2021), no. 5, 1470–1485. (published version) (arXiv)
12. KSBA compactification of the moduli space of K3 surfaces with a purely non-symplectic automorphism of order four (with H.-B. Moon). Proceedings of the Edinburgh Mathematical Society (2) 64 (2021), no. 1, 99–127. (published version) (arXiv)
13. Equations for point configurations to lie on a rational normal curve (with A. Caminata, N. Giansiracusa, H.-B. Moon). Advances in Mathematics 340 (2018), 653–683. (published version) (arXiv) (minor correction)
14. K3 surfaces with \(\mathbb{Z}_2^2\) symplectic action. Rocky Mountain Journal of Mathematics 48 (2018), no. 7, 2347–2383. (published version) (arXiv)
15. The KSBA compactification of the moduli space of \(D_{1,6}\)-polarized Enriques surfaces. Mathematische Zeitschrift 300 (2022), no. 2, 1819–1850. (published version) (arXiv)
16. On the cone of effective 2-cycles on \(\overline{M}_{0,7}\). European Journal of Mathematics 1 (2015), no. 4, 669–694. (published version) (arXiv)