Research
Research
I'm interested in derived categories and noncommutative geometry, with interests in mirror symmetry and Bridgeland stability conditions.
Lately I've been thinking about non-commutative deformations of curves in Calabi-Yau threefolds, homological mirror symmetry questions for singular del Pezzo surfaces, invariants of Enriques surfaces and their derived categories.
All my papers can be found on my arxiv page.
G. Gugiatti, F. Rota, On the mirrors of low-degree del Pezzo surfaces, 2025 (arxiv)
H. Dell, A. Jacovskis, F. Rota, Cyclic covers: Hodge theory and categorical Torelli theorems, Int. Mat. Res. Not., 2025 (pdf, journal, arxiv);
R. Moschetti, F. Rota, L. Schaffler, The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces, Doc. Math., 2024 (pdf, journal, arxiv);
B. Lim, F. Rota, Orbifold Semiorthogonal Decompositions for Abelian Varieties, J. Noncommut. Geom., 2024 (pdf, journal, arxiv);
G. Gugiatti, F. Rota, Full exceptional collections for anticanonical log del Pezzo surfaces, Int. Mat. Res. Not., 2023 (pdf, journal, arxiv);
B. Lim, F. Rota, Riemann-Roch coefficients for Kleinian orbisurfaces, Boll. Unione Mat. Ital., 2023 (pdf, journal, arxiv);
M.Petkovič, F. Rota, A note on the Kuznetsov component of the Veronese double cone, J. Pure Appl. Algebra, 2023 (pdf, journal, arxiv);
R. Moschetti, F. Rota, L. Schaffler, A computational view on the non-degeneracy invariant for Enriques surfaces, Experimental Mathematics, 2022 (pdf, journal, arxiv, code);
M. Altavilla, M. Petkovič, F. Rota, Moduli spaces on the Kuznetsov component of Fano threefolds of index 2, Épijournal de Géométrie Algébrique, 2022 (pdf, journal, arxiv);
F. Rota, The stability manifold of local orbifold elliptic quotients, J. London Math. Soc., 2022 (pdf, journal, arxiv);
B. Lim, F. Rota, Characteristic classes and stability conditions for projective Kleinian orbisurfaces, Math. Z., 2021 (pdf, journal, arxiv);
F. Rota, Some Quot schemes in tilted hearts and moduli spaces of stable pairs, Internat. J. Math., 2021 (journal, arxiv);
S. Filipazzi, F. Rota, An example of Berglund-Hübsch mirror symmetry for a Calabi-Yau complete intersection, Le Matematiche, 2018 (journal, arxiv).