Research |
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”. To appear in Rev. Mat. Complutense.
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.
Preprints
-
A. Bravo, S. Encinas, J. Guillán-Rial, “On some properties of the
asymptotic Samuel function”.
-
J.M. Aldaz, A. Bravo, H. Render, “Te apolar inner product and Bombieri
type inequality for polynomials”.