Academic at the Department of Mathematics of the Universidad Técnica Federico Santa María, Valparaíso, Chile.

Research
I am mainly interested in birational geometry. More precisely, in asymptotic invariants and positivity in algebraic geometry (such as Newton-Okounkov bodies) and the use of techniques from the Minimal Model Program to the classification of algebraic varieties (e.g. Fano varieties). I am also interested in algebraic group actions on algebraic varieties.
(Pre)publications
Here you can find my research articles.
► "On singular Fano varieties with a divisor of Picard number one" (arXiv:1605.08307)
Annali della Scuola Normale Superiore di Pisa (5), XIX (2), pages 567–600, 2019.
DOI: 10.2422/2036-2145.201609_018.
► "Newton-Okounkov bodies on projective bundles over curves" (arXiv:1703.06828)
Mathematische Zeitschrift, 291 (3–4), pages 1357–1379, 2019.
DOI: 10.1007/s00209-018-2173-3.
► "Fano threefolds as equivariant compactifications of the vector group" (arXiv:1802.08090)
Joint with Zhizhong Huang at Klosterneuburg.
Michigan Mathematical Journal, 69 (2), pages 341-368, 2020.
DOI: 10.1307/mmj/1576033218.
► "A characterization of some Fano 4-folds through conic fibrations" (arXiv:1803.09129)
Joint with Eleonora Anna Romano at Genova.
International Mathematics Research Notices, 2021 (16), pages 12009-12036, 2021.
DOI: 10.1093/imrn/rnz244.
► "Equivariant compactifications of vector groups with high index" (arXiv:1806.02010)
Joint with Baohua Fu at Beijing.
Comptes Rendus Mathématique, 357 (5), pages 455–461, 2019.
DOI: 10.1016/j.crma.2019.05.002.
► "On the liftability of the automorphism group of smooth hypersurfaces of the projective space" (arXiv:2004.12455)
Joint with Víctor González-Aguilera at Santiago and with Álvaro Liendo at Talca.
To appear in Israel Journal of Mathematics.
DOI: 10.1007/s11856-022-2417-0.
► "Projective manifolds whose tangent bundle is Ulrich" (arXiv:2108.13944)
Joint with Vladimiro Benedetti at Dijon, Yulieth Prieto at Trieste and Sergio Troncoso at Valparaíso.
Journal of Algebra, Volume 630, 15 September 2023, Pages 248-273.
DOI: 10.1016/j.jalgebra.2023.03.046.
► "Del Pezzo quintics as equivariant compactifications of vector groups" (arXiv:2209.04152)
Joint with Adrien Dubouloz at Dijon and Takashi Kishimoto at Saitama.
► "On a Torelli Principle for automorphisms of Klein hypersurfaces" (arXiv:2212.13308)
Joint with Víctor González-Aguilera at Santiago, with Álvaro Liendo at Talca, and Roberto Villaflor at Santiago.
Currently, I am partially suppported by the following grants:
► "Birational geometry and vector bundles on varieties with many automorphisms"
(Fondecyt Regular 1231214, Principal Investigator, 2023 - 2026).
Together with Álvaro Liendo as Co-Investigator.
► "Normal varieties with torus actions: equivariant compactifications of certain solvable groups and singularities"
(Fondecyt Regular 1200502, Co-Investigator, 2020 - 2023).
Together with Álvaro Liendo (PI) and Maximiliano Leyton-Álvarez (CI).
Previously, I was supported by the following grant:
► "Linear systems and birational geometry of varieties of Fano type"
(Fondecyt Iniciación 11190323, Principal Investigator, 2019 - 2021).
Teaching
MAT529 ("Aritmética", i.e., Teoría Algebraica de Números): (2023-1).
MAT426 (Curvas Algebraicas): (2020-2), (2021-2), (2023-2). ¿Te interesa? Haz click aquí.
MAT290 (Geometría Diferencial): (2022-2).
MAT235 (Variable Compleja): (2021-2), (2022-2).
MAT214 (Estructuras Algebraicas): (2019-1), (2021-1), (2023-1).
MAT210 (Álgebra Lineal): (2020-1).
MAT060 (Álgebra y Geometría): (2019-1), (2022-1).
Students
Graduate: ► Felipe Valladares (co-directed by Gabriele Ranieri). Introducción a la Teoría de Esquemas Afines (15/01/2020). ► Tobías Martínez (co-directed by Sebastián Herrero). Counting rational points and related classification problems in Algebraic Geometry (ongoing).
Undergraduate: ► Eduardo Núñez. Teorema de los números primos (10/12/2020). ► Gustavo Arcaya. Einstein metrics and Geometry of the complex Monge-Ampère equation (09/06/2022). ► Fabián Levicán. A computational approach to classification of additive smooth Fano polytopes (20/01/2023). ► Cristóbal Montecino. Quantum cohomology, Gromov-Witten invariants and String theory (ongoing). ► Lucas Montero (co-directed by Dardo Goyeneche). Algebraic geometry codes applied to Quantum information (ongoing). ► Emilio Oyanedel (co-directed by Roberto Villaflor Loyola). The moduli space of polarized K3 surfaces (ongoing).
Research assistant (i.e., Introduction to advanced topics in Algebraic Geometry): ► Gustavo Arcaya. Hodge Theory on Kähler manifolds (2020). ► Cristóbal Montecino. Enumerative geometry, Quantum cohomology and String theory (2021). ► Emilio Oyanedel. K3 surfaces and Torelli Theorem (2022). ► Sebastián Fuentes. Complex Algebraic Surfaces with a view towards the Minimal Model Program (2022, ongoing). ► Mario Pastrana. Complex Algebraic Surfaces with a view towards the Minimal Model Program (2022, ongoing).
About me
A brief CV
Born on February 28th, 1991 in Copiapó (Chile)
Since December 2018 : Academic (Profesor Instructor) at the Department of Mathematics of the Universidad Técnica Federico Santa María, Valparaíso, Chile.
2018 : Postdoctoral Researcher at AMSS in the Chinese Academy of Sciences, Beijing.
2017 : ATER at Université Grenoble Alpes, Grenoble.
2014-2017 : Université Grenoble Alpes, Grenoble, PhD in Mathematics.
2013-2014 : Université Joseph Fourier, Grenoble, Master 2 Research in Mathematics.
2011-2013 : Universidad Técnica Federico Santa María, Valparaíso, Master in Mathematics.
2009-2011 : Universidad Técnica Federico Santa María, Valparaíso, Undergraduate degree in Mathematics.
2008 : Colegio Salesiano Valparaíso, Valparaíso, scientific formation.
Theses in mathematics
- PhD thesis: « Geometry of singular Fano varieties and projective bundles over curves » .
Advisors : Stéphane Druel and Catriona Maclean. Institut Fourier, Grenoble.
Thesis defence : october 2017. - Master 2 thesis: « Rationnally connected varieties and their behavoir in family » .
Advisor : Catriona Maclean. Institut Fourier, Grenoble.
Thesis defence : june 2014. - Master thesis: « On the automorphism group of complete intersections of type (2,3) ».
Advisor : Víctor González-Aguilera. Universidad Técnica Federico Santa María, Valparaíso.
Thesis defence : july 2013. - Undergraduate thesis: « Complex algebraic surfaces of type K3 ».
Advisor : Víctor González-Aguilera. Universidad Técnica Federico Santa María, Valparaíso.
Thesis defence : july 2011. - Groupe de travail 2016-2017 sur les Champs algébriques, based on several references, including the book of Neumann Algebraic Stacks and Moduli of Vector Bundles.
- Groupe de travail 2015-2016 sur les Surfaces algébriques complexes, based on the book of Beauville Surfaces algébriques complexes.
- Groupe de travail 2014-2015 sur les Déformations et les Espaces de Modules, based on the book of Hartshorne Deformation Theory.
- Seminar on Algebraic Transformation Groups, HSE University, Russia. February 2023.
- 15th ALGA (Commutative Algebra and Algebraic Geometry), IMPA, Brazil. February 2023.
My recent activities
Here is a list of some of my recent activities.
Working groups
I actively participate in the Algebraic Geometry Seminar organized by Giancarlo Urzúa (PUC Chile). For further information, click here.
On 2022, Sergio Troncoso (UTFSM) and I, we organized a reading group on riemannian geometry. During the semester 2022-1 we will discuss the basics on riemannian geometry and we followed the lecture notes of Olivier Biquard. For further information, click here.
On 2019, Gonzalo Manzano (USACH) and I, we organized a reading group on algebraic geometry. During the semester 2019-1 we discussed the basics on algebraic geometry and we followed the lecture notes of Joseph Le Potier. For further information, click here.
I organized, along with Louis-Clément, our own working group for PhD students. The goal was to read a book together and give a talk each week. Every year we worked on a quite large topic around complex algebraic geometry.
Recent talks and Conferences
Contact
E-mail : pedro [dot] montero [at] usm [dot] cl
Phone : (+56) 32 2654640
Office F247
Departamento de Matemática
Universidad Técnica Federico Santa María
Avenida España 1680, Valparaíso, Chile