# Andrea Petracci

I am a tenure-track assistant professor (RTD-B) at the
Department of Mathematics
of Università di Bologna.

Previously I worked at
Freie Universität
Berlin in the group of Klaus Altmann.

I graduated from Imperial College London in September 2017 and my advisor was Alessio Corti.
Before that I studied in Pisa (Italy).

Here is my CV.

Here is my Google
Scholar profile.

My institutional e-mail address for teaching:

a [dot] petracci [at] unibo [dot] it

My permanent e-mail address for research:

andrea [dot] petracci [at] alumni [dot] sns [dot] it

Here is my institutional website.

Address: Dipartimento di Matematica

Università di Bologna

Piazza di Porta San Donato 5

40126 Bologna

Italy

### Where I'll be

Mar 2022: Toric geometry, Oberwolfach, Germany

Jul 2022: Group actions in algebraic geometry, Cetraro, Italy

Aug 2022: Stability and Moduli, Stony Brook, US

Oct 2022: Toric Degenerations and Mirror Symmetry, Kumamoto, Japan

Nov 2022: Birational Geometry and K-stability of Fano Varieties, Edinburgh, UK

Dec 2022: Toric degenerations, BIRS, Banff, Canada

Jan 2023: K-stability of Fano varieties and birational invariants, Trento, Italy

Feb 2023: Explicit Moduli Problems in Higher Dimensions, BIRS, Banff, Canada

### Research

The area of my work is algebraic geometry. My interests lie in the classification problem of Fano varieties and their moduli. I am especially interested in toric geometry, deformation theory, Gromov-Witten theory and the Gross-Siebert program.

Here is the list of my works:

- (with Liana Heuberger)
*On K-moduli of Fano threefolds with degree 28 and Picard rank 4*.

arXiv:2303.12562 -
(with Antonella Grassi, Giulia Gugiatti, Wendelin Lutz)
*Reflexive polygons and rational elliptic surfaces*.

doi.org/10.1007/s12215-023-00922-3 arXiv:2302.05751 - (with Hamid Abban, Ivan Cheltsov, Alexander Kasprzyk, Yuchen Liu)
*On K-moduli of quartic threefolds*.

arXiv:2210.14781 - (with Simon Felten and Sharon Robins)
*Deformations of log Calabi-Yau pairs can be obstructed*. To appear in Math. Res. Lett.

arXiv:2109.00420 *K-moduli of Fano 3-folds can have embedded points*

arXiv:2105.02307*On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties*. Trans. Amer. Math. Soc. 375 (2022), no. 8, 5617–5643.

doi.org/10.1090/tran/8636 arXiv:2105.01174*A 1-dimensional component of K-moduli of del Pezzo surfaces*. In: I. Cheltsov, X. Chen, L. Katzarkov, J. Park (eds), Birational Geometry, Kähler-Einstein Metrics and Degenerations, Springer Proceedings in Mathematics & Statistics, vol 409, Springer.

doi.org/10.1007/978-3-031-17859-7_36 arXiv:2102.13510- (with Yuchen Liu)
*On K-stability of some del Pezzo surfaces of Fano index 2*. Bull. London Math. Soc. 54 (2022), no. 2, 517-525

doi.org/10.1112/blms.12581 arXiv:2011.05094 - (with Simon Felten)
*The logarithmic Bogomolov-Tian-Todorov theorem*. Bull. London Math. Soc. 54 (2022), no. 3, 1051-1066

doi.org/10.1112/blms.12613 arXiv:2010.13656 - (with Anne-Sophie Kaloghiros)
*On toric geometry and K-stability of Fano varieties*

Trans. Amer. Math. Soc. Ser. B (2021), no. 8, 548-577.

doi.org/10.1090/btran/82 arXiv:2009.02271 - (with Alessio Corti and Matej Filip)
*Mirror Symmetry and smoothing Gorenstein toric affine 3-folds*. In: Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday (2022), London Mathematical Society Lecture Note Series, pp. 132-163, Cambridge University Press. doi.org/10.1017/9781108877831.005 arXiv:2006.16885 *On deformations of toric Fano varieties*. In: A.M. Kasprzyk, B. Nill (eds), Interactions with Lattice Polytopes, Springer Proceedings in Mathematics & Statistics, vol 386, Springer.

doi.org/10.1007/978-3-030-98327-7_14 arXiv:1912.01538*An example of Mirror Symmetry for Fano threefolds*. In Birational Geometry and Moduli Spaces, Springer INdAM Series (2020).

doi.org/10.1007/978-3-030-37114-2_10 arXiv:1901.06155*Some examples of non-smoothable Gorenstein Fano toric threefolds*

Math. Zeit. (2020), no. 295, 751-760.

doi.org/10.1007/s00209-019-02369-8 arXiv:1804.07960*Homogeneous deformations of toric pairs*. Manuscripta Math. (2021), no. 166, 37-72.

doi.org/10.1007/s00229-020-01219-w arXiv:1801.05732- (with Alessandro Oneto)
*On the quantum periods of del Pezzo surfaces with 1/3(1,1) singularities*. Adv. Geom. 18 (2018), no. 3, 303-336.

doi.org/10.1515/advgeom-2017-0048 arXiv:1507.08589 - (with Mohammad Akhtar, Tom Coates, Alessio Corti, Liana Heuberger, Alexander Kasprzyk,
Alessandro Oneto, Thomas Prince, Ketil Tveiten)
*Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces*. Proc. Amer. Math. Soc. 144 (2016), no. 2, 513-527.

doi.org/10.1090/proc/12876 arXiv:1501.05334

### Theses

My PhD thesis about Mirror Symmetry for Fano varieties and for singularities, written under the supervision of Alessio Corti (Imperial College London), September 2017My MSc thesis about the moduli stack of curves and hyperelliptic curves, written under the supervision of Angelo Vistoli (Scuola Normale Superiore di Pisa), March 2013

My BSc thesis (in Italian) about the Lefschetz hyperplane theorem, written under the supervision of Rita Pardini (Università di Pisa), July 2010

### Talks

Here there are the recordings of some of my research talks:- Introduction to toric geometry, Apr 2021
- Toric geometry and singularities on K-moduli, Dec 2020
- On deformations and smoothings of toric Fano varieties and of toric singularities (joint talk with Helge Ruddat), Sep 2020
- K-moduli stacks and K-moduli spaces of Fano varieties can be singular, Aug 2020

### Teaching at Università di Bologna

Spring 2023: lectures of Scheme Theory, exercise classes of Topology

Spring 2022: lectures of Scheme Theory, exercise classes of Topology

Autumn 2021: some lectures of Linear Algebra for engineers

### Teaching at Freie Universität Berlin

Summer Semester 2021: course/seminar of topics in Algebraic Geometry (Seminar "Forschungsmodul Algebra/Algebraische Geometrie"),

research seminar of Algebraic Geometry (Forschungsseminar),

exercises classes of Algebraic Geometry (Zentralübung von Algebra II)

Winter Semester 2020/21: course of Computer Algebra

Summer Semester 2020: lectures and exercise classes of Funktionentheorie (Complex Analysis)

Winter Semester 2019/20: course of Computer Algebra

Summer Semester 2019: lectures and exercise classes of Funktionentheorie (Complex Analysis)

Winter Semester 2018/19: exercise classes of Algebra I (Commutative Algebra)

### Other documents

A poster about Kontsevich formula of plane rational curves and Gromov-Witten invariants, written together with Francesca CarocciA poster about Mirror Symmetry and Fano varieties

Some slides (in Italian) on the moduli stack of curves and hyperelliptic curves, May 2013

Some slides (in Italian) on Cayley-Bacharach properties in algebraic geometry, May 2011

### Other activities

In December 2023, together with Enrico Fatighenti, I created an Algebraic Geometry Advent Calendar.In September 2023 I am co-organising an algebraic geometry workshop in Bologna.

In September 2019 I co-organised the opening conference of the thematic Einstein semester on algebraic geometry, which was held in Berlin in the winter semester 2019/20.

In July 2018, together with Tom Ducat I organised a workshop in Nottingham about cluster algebras and algebraic geometry.

In the academic year 2014-2015, together with Lars Sektnan, I organised the Junior Geometry Seminar at Imperial College.

In April 2014 I co-organised the Traumatic Workshop: Birational Geometry and Fano Varieties at Imperial College.

In December 2013, together with Andrea Fanelli, I took photos for the charity calendar of the geometry group of Imperial College.