In February 2012, I completed my Ph.D. in Mathematics at the Università degli studi Roma TRE with a thesis entitled Syzygies, Pluricanonical Maps and the Birational Geometry of Irregular Varieties, written under the supervision of Prof. G. Pareschi (Università degli studi di Roma "Tor Vergata").
Before entering in the Ph.D. program of the Università degli Studi Roma TRE, I was a student at the University of Bologna where I completed both my B.Sc. in Mathematics (2006) and M.Sc. in Mathematics (2008).
My primary field of interest is the study of Algebraic Geometry with cohomological methods.
I have currently two ongoing projects. On one side, I study derived categories and derived invariants of algebraic varieties defined over fields of positive characteristic. On the other side, I am working on finding an effective birational characterization of semiabelian varieties.
Publications and Preprints:
- A footnote to a theorem of Kawamata (With M. Mendes Lopers and R. Pardini). To appear on Math. Nach.
- Effective characterization of quasi-abelian surfaces (With M. Mendes Lopes and R. Pardini). To appear on Forum Math. Sigma
- Counting Twisted Tame Fourier-Mukai Partners of an Ordinary K3 Surface (With T. Srivastava). To appear on MRL.
Published research papers:
- On the Brauer Group of Bielliptic Surfaces (With E. Ferrari, M. Vodrup, and an Appendix with J. Bergström). Documenta Matematica 2022.
- On Ordinary Enriques Surfaces in Positive Characteristic (with R. Laface). Nagoya math Journal 2020.
- Theta-regularity and log-canonical threshold (With M. Ø ygarden). Mathematica Scandinavica 2021.
- Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic. Mathematical Research Letter 2021.
- Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic (With K. Honigs and L. Lombardi). Math Z 2019
- A note on the derived category of Enriques surfaces in characteristic 2. Bollettino dell'Unione Matematica Italiana (2016). DOI:10.1007/s40574-016-0100-2
- Deformations of minimal cohomology classes on abelian varieties. (With L. Lombardi). Communications in Contemporary Mathematics DOI:10.1142/S0219199715500662
- GV-Schemes and their embeddings in principally polarized abelian varieteis. (With L. Lombardi). Mathematische Nachrichten, DOI: 10.1002/mana.201400238
- Characterization of products of theta divisors. (With Z. Jiang and M. Lahoz). Compositio Mathematica150 (2014): 1384-1412.
- Syzygies and Equations of Kummer Varieties. Bulletin of London Mathematical Society (2013) 45 (3):651-665.
- On the Iitaka Fibration of Varieties of Maximal Albanese Dimension. (With Z. Jiang and M. Lahoz) International Mathematics Research Notices, (2012).
- On the Tetracanonical Map of Varieties of General Type and Maximal Albanese Fimension. Collectanea Mathematica, (2011).
- Derived Categories of Fano Toric 3-folds via Frobenius Morphism. (With A. Bernardi) Le Matematiche, Volume: LXIV, Issue: II (2010).
A selection from Stockholm University publication database
Theta-regularity and log-canonical threshold
2020. Morten Øygarden, Sofia Tirabassi. Mathematica Scandinavica 126 (1), 73-81Article
We show that an inequality, proven by Küronya-Pintye, which governs the behavior of the log-canonical threshold of an ideal over Pn and that of its Castelnuovo-Mumford regularity, can be applied to the setting of principally polarized abelian varieties by substituting the Castelnuovo-Mumford regularity with Θ-regularity of Pareschi-Popa.
Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic
2020. Katrina Honigs, Luigi Lombardi, Sofia Tirabassi. Mathematische Zeitschrift 295, 727-749Article
We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable sheaves. We apply this fact to show that the set of Fourier–Mukai partners of a canonical cover of a hyperelliptic or Enriques surface over an algebraically closed field of characteristic greater than three is trivial. These results extend earlier results of Bridgeland–Maciocia and Sosna to positive characteristic.
ON ORDINARY ENRIQUES SURFACES IN POSITIVE CHARACTERISTIC
2020. Roberto Laface, Sofia Tirabassi. Nagoya mathematical journalArticle
We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.
Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic
2021. Katrina Honigs, Max Lieblich, Sofia Tirabassi. Mathematical Research Letters 28 (1), 65-91Article
We prove that a twisted Enriques (respectively, untwisted bielliptic) surface over an algebraically closed field of positive characteristic at least 3 (respectively, at least 5) has no non-trivial Fourier-Mukai partners.
GV-subschemes and their embeddings in principally polarizedabelian varieties
2015. Luigi Lombardi, Sofia Tirabassi. Mathematische Nachrichten 288 (11-12), 1405-1412Article
We prove that any embedding of a GV -subscheme in a principally polarized abelian variety does not factorthrough any nontrivial isogeny. As an application, we present a new proof of a theorem of Clemens–Griffithsidentifying the intermediate Jacobian of a smooth cubic threefold to the Albanese variety of its Fano surface oflines.
On the Brauer group of bielliptic surfaces (with an appendix by Jonas Bergström and Sofia Tirabassi)
2022. Eugenia Ferrari (et al.). Documenta Mathematica 27, 383-425Article
We provide explicit generators of the torsion of the second cohomology of bielliptic surfaces, and we use this to study the pullback map between the Brauer group of a bielliptic surface and that of its canonical cover.