ANA BRAVO ZARZA

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Algebra Seminar

Research interests: Commutative algebra, Algebraic geometry: resolution of singularities, Rees algebras, Arc spaces.

Publications:

1.  J.M. Aldaz, A. Bravo, S. Gutierrez, A. Ubis, “A Theorem of D.J. Newman on Eulers phi function and arithmetic progressions”, Amer. Math. Monthly, 108,4 (2001)  364-367.

2.  A. Bravo, O.E. Villamayor U., “Strengthening the Theorem of Embedded desingularization”, Math. Res. Letters, 8 (2001) 79-90.

3. A . Bravo, O.E. Villamayor U., “Smoothness and tangent bundles of arithmetical schemes”, Math. Z. 239,1  (2001) 159-182.

4. A. Bravo, K. Smith, “Behavior of test ideals under smooth and étale homomorphisms”, J. Algebra  247,1 (2002) 78-94.

5.  A. Bravo, “Quasi-smoothness and arithmetical surfaces”, J. Pure and App. Algebra, 170, 2-3 (2002) 145-173.

6. J.M. Aldaz, A. Bravo, “Perspectivas en la Teoría de los números”, Margarita Matemática en memoria de Jose Javier (Chicho) Guadalupe Hernandez, 247,1 273-282.

7.  A. Bravo, O.E. Villamayor U., “A strengthening of resolution of singularities in characteristic zero”, Proc. London Math. Soc., 86 (2003) 327-357.

8. J.M. Aldaz, A. Bravo, “Euclid’s argument on the infinitude of primes”, Amer. Math. Monthly, 110 (2003) 141-142.

9. A. Bravo, “Canonical subalgebra bases”, Trends in commutative algebra, ed. L.  Avramov et al, MSRI Publications, 51, Cambridge University Press, New York 2004, 249-256.

10. A. Bravo, S. Encinas, O.E. Villamayor, “A simplified proof of desingularization and applications”, Rev. Mat. Iberoamericana, 21,2 (2005) 349-458.

11. A. Bravo, H. Hauser, Book Review: “Resolution of Curve and Surface Singularities by K. Kiyek and J.L. Vicente. Algebras and Appplications, vol 4, Kluwer Academic Publishers 2004”, Bull. Amer. Math. Soc., 43 (2006) 241-247.

12.  A. Bravo, O.E. Villamayor U., “Singularities in positive characteristic, stratification and simplification of the singular locus”, Adv. in Math., 224 (2010) 1349-1418.

13.  A. Bravo, O.E. Villamayor U.,” Elimination algebra and inductive arguments in resolution of singularities”, The Assian Journal of Mathematics, 15,3

(2011) 321-356. Special volume in honor of H. Hironaka.

14. A. Bravo, M.L. García Escamilla, O.E. Villamayor U., “On Rees algebras and invariants of singularities over perfect fields”, Indiana University

Math. Journal, 61 (3) (2012) 1201-1251.  

15. A. Bravo, "A remark on Strong Factorizing Resolutions", Revista de la Real Academia de Ciencias Exactas,

Físicas y Naturales, 107 (2013) 53-60.   

16. A. Bravo, O. E. Villamayor U., "On the behavior of the multiplicity on schemes: stratifications and blow-ups". The Resolution of Singular Algebraic Varieties, Clay Mathematics proceedings, vol 20, pp. 81-207;  Edited by: David Ellwood, Harvard University, Cambridge, MA, Herwig Hauser, Universtitat Wien, Vienna, Austria, Shigefumi Mori, RIMS, Kyoto University, Japan, and Josef Schicho, Austrian Academy of Sciences, Linz, Austria. AMS-Clay Mathematics Institute, 2014. ISBN-13: 978-0-8218-8982-4.

17. A. Bravo, S. Encinas, B. Pascual-Escudero, “Nash multiplicities and resolution invariants”, Collect. Math., 68 (2017) 175-217.

18. C. Abad, A. Bravo, O. E. Villamayor U., “Finite morphisms and simultaneous reduction of the multiplicity”, Math. Nachr., 293 (2020) 8-38.

19. A. Bravo, S. Encinas, B. Pascual-Escudero, “Nash multiplicity sequences and Hironaka’s order function”, Indiana U. Math. Journal, 69 (6) (2020) 1933-1973.

20. A. Bravo, S. Encinas, B. Pascual-Escudero, “Contact loci and Hironaka’s order”, Manuscripta Math., 166 (2021) 131-165.

21. A. Bravo, S. Encinas, “Finite morphisms and Nash multiplicity sequences”, J. Pure and App. Algebra, 225 (2021) (11). Paper No. 106728, 18 pp.

22. A. Benito, A. Bravo, S. Encinas, “The asymptotic Samuel function and invariants of singularities”. Rev. Mat. Complutense, 37 (2) 2024 603-652. Correction: 653-654.

23. A. Bravo, S. Encinas, “Hilbert-Samuel multiplicity and finite projections”. Handbook of Singularities, vol 4. Editors J. L. Cisneros-Molina, Lê Dũng Tráng and J. Seade. ISBN 978-3-031-31924-2 (printed version) 978-3-031-31925-9 (eBook version). 2023.

24. J.M. Aldaz, A. Bravo, H. Render, “The apolar inner product and Bombieri type inequality for polynomials”. To appear in Journal of Inequalities and Applications.

Preprints

- A. Bravo, S. Encinas, J. Guillán-Rial, “On some properties of the asymptotic Samuel function”.

- A. Bravo, María de la Paz Tirado Hernández, “Finiteness of leaps in the sense of Hasse-Schmidt of reduced rings”.

Others

-“Contact loci and Hironaka’s order “, Oberwolfach report 06/2019, Workshop “Singularities and Homological aspects in Commutative Algebra”. DOI: 10.4171/OWR/2019/6.

-“The asymptotic Samuel function: some properties and invariants of singularities”, Oberwolfach report 06/2023, Workshop “Resolutions in Local Algebra and Singularity Theory”. DOI: 10.4171/OWR/2023/6.