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

Beijing

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 Yulieth Prieto at Trieste and Sergio Troncoso at Valparaíso. With an Appendix by Vladimiro Benedetti at Dijon.
"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.

I am partially suppported by Fondecyt Grants "Linear systems and birational geometry of varieties of Fano type" (Fondecyt Iniciación 11190323, Principal Investigator, 2019 - 2021) and "Normal varieties with torus actions: equivariant compactifications of certain solvable groups and singularities" (Fondecyt Regular 1200502, Co-Investigator (with Álvaro Liendo (PI) and Maximiliano Leyton-Álvarez (CI)), 2020 - 2023).

Teaching

MAT426 (Curvas Algebraicas): (2020-2), (2021-2), (2023-2). Nuevo¿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).

MAT212 ("Álgebra Abstracta II", i.e., Teoría Algebraica de Números): (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).

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.

    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

    • The 20th Affine Algebraic Geometry (AAG) Meeting, Saitama University, Japan. March 2022.
    • Geometry, Arithmetic and Differential Equations of Periods (GADEPs), IMPA, Brazil. April 2022.

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


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