Research

Publications

1. T. Ducat, Quartic surfaces up to volume preserving equivalence, Selecta Math., 30(2) (2024) (journal / arXiv)

2. T. Ducat, The 3-dimensional Lyness map and a self-mirror log Calabi-Yau 3-fold. manuscripta math. (2023), 54pp. (journal / arXiv)

3. T. Ducat, The tropicalisation of a (-2,0)-flop. to appear in "Proceedings of the Nottingham Seminar", L. Campo, J, Hofscheier, A. Kasprzyk (Eds.), Springer Proceedings in Mathematics and Statistics, Springer. (arXiv) 

4. G. Brown, T. Coates, A. Corti, T. Ducat, L. Heuberger, A. Kasprzyk, Computation and data in the classification of Fano varieties, In Y.-H. He, M.-L. Ge, C.-M. Bai, J. Bao & E. Hirst (Eds.), Nankai Symposium on Mathematical Dialogues: Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern, Springer, 2022. (journal / arXiv) 

5. T. Ducat, Mori flips, cluster algebras and diptych varieties without unprojection. In H. Abban, G. Brown, A. Kasprzyk, & S. Mori (Eds.), Recent Developments in Algebraic Geometry: To Miles Reid for his 70th Birthday (LMS Lect. Note Series), 116-149.  (journal / pdf)

6. S. Coughlan, T. Ducat, Constructing Fano 3-folds from cluster varieties of rank 2. Compositio Mathematica, 156(9) (2020), 1873-1914. (journal / arXiv / codim 4 & codim 5 tables)

7. T. Ducat, I. Hedén, S. Zimmermann, The decomposition groups of plane conics and plane rational cubics. Math. Res. Lett., 26(1) (2019), 35-52. (journal / arXiv)

8. T. Ducat, Constructing Q-Fano 3-folds à la Prokhorov & Reid. Bull. London Math. Soc., 50(3) (2018), 420-434. (journal / arXiv)

9. T. Ducat, Divisorial extractions from singular curves in smooth 3-folds. Int. J Math., 27(1) (2016), 23pp. (journal / arXiv)

Preprints

1. O. Daisey, T. Ducat, A Laurent phenomenon for the Cayley plane. (arXiv)

2. T. Ducat, Divisorial extractions from singular curves in a smooth 3-fold, II: low codimension. (arXiv)

PhD thesis

T. Ducat, Mori extractions from singular curves in a smooth 3-fold. (pdf)

Fun Stuff

Equiangular lines and del Pezzo surfaces. (pdf)

The Mathematics of Dobble. (Slides for a talk given at an open day.) (pdf)