César Lozano Huerta

    My area of research is algebraic geometry. That is, zeros of polynomials.
    I use modern tools and language to study questions that can be traced back
    to the 19th or early 20th century.
    People tend to call this sub discipline of mathematics
    classical algebraic geometry



    Seminario nacional de geometría algebraica en LÍNEA: (WWW)


    Jornadas de geometría algebraica: (WWW)



    Publications -- research

    1. Birational geometry of linear determinantal quartic 3-folds and rationality. (arXiv, 2025)
      joint with M. Leal and M. Vite
      Comments welcome.

    2. Geometry of syzygies of sheaves on P2 via interpolation and Bridgeland stability. (arXiv, 2024)
      joint with M. Leal and Tim Ryan.
      Submitted.

    3. The Noether-Lefschetz locus of surfaces in P3 formed by determinantal surfaces. (arXiv, 2023)
      joint with M. Leal and M. Vite.
      Mathematische Nachrichten (2024), Vol. 297, Issue 12.
      Supplementing Macaulay2 code: (here)

    4. Minimal free resolutions of sheaves on the plane and the base locus of their moduli space. (arXiv, 2021)
      joint with M. Leal and T. Ryan.
      Superseded by (arXiv)

    5. On the weak Lefschetz principle in birational geometry. (arXiv), (AMS)
      joint with A. Massarenti.
      Notices of the American Mathematical Society, 2021.

    6. On the position of nodes of plane curves. (arXiv)
      joint with T. Ryan.
      Bulletin of the Australian Mathematical Society (2021), Vol. 103, Issue 1.

    7. The Lefschetz principle in birational geometry: birational twin varieties (arXiv)
      joint with A. Massarenti.
      Birational Geometry and Moduli spaces, Springer INdAM Series (2020), Vol. 39, 109--132.

    8. On the birational geometry of Hilbert schemes of points and Severi divisors (arXiv)
      joint with T. Ryan.
      Communications in Algebra (2020), Vol. 48, Issue 11, 4596?4614.

    9. Families of elliptic curves and Bridgeland stability: (arXiv)
      joint with B. Schmidt, P. Gallardo.
      Michigan Mathematical Journal (2018), Vol. 67, Issue 4, 787-813

    10. Extremal higher codimension cycles of the space of complete conics: (arXiv)
      Contemporary Mathematics (2018), Vol. 709, 87-99

    11. Seed to seedling transitions in successional habitats across a tropical landscape.
      Join with M. de la Peña-Domene, H. F. Howe, E. Cruz-León, R. Jiménez-Rolland, C. Martínez-Garza.
      OIKOS. Volume 126, Issue 3, 2017.
      doi/10.1111/oik.03394

    12. Birational geometry of complete quadrics: (arXiv)
      International Mathematics Research Notices (2015), Vol. 2015, 12563-12589.

    13. Birational geometry of the space of complete quadrics,
      PhD Thesis, University of Illinois at Chicago, 2014.

      Publications -- literacy

    14. Tres medallas de la geometría birracional: (WWW)
      Motivos Matemáticos, Instituto de matemáticas, UNAM, 2018.

    15. Clases Características (J. W. Milnor y J. D. Stasheff )
      Princeton University Press and University of Tokio Press, 1974.
      Traducción al español de César Lozano Huerta y Mauricio Bustamante.
      Colección Papirhos, Serie Textos. UNAM, 2017.

    16. Curvas algebraicas y la pregunta de Halphen: (arXiv)
      Miscelánea Matemática de la SMM, Vol. 62, 2016.


      My previous universities:
      UIC | CINVESTAV | UTAH | HARVARD