Advanced search
Start date

The relation between toric geometry, theory of local blow-ups and ramification theory and their applications in valuation theory


The main goal of this research project is to expand the knowledge of the relation between toric geometry, theory of local blow-ups and ramification theory. The motivation for this study is the common applications of these areas to valuation theory, more specifically to the local uniformization problem. The local uniformization problem (that can be seen as a local version of resolution of singularities) is open for valuations centered on algebraic varieties over a field of positive characteristic. However, in the recent years, many programs to solve this problem have gainned strength. Three of the most important are those developed by Teissier (using toric geometry), by Spivakovsky (using theory of local blow-ups) and by Knaf and Kuhlmann (using ramification theory). The problems which will be studied in this project will allow us to adapt strategies from each of these programs to the others. This will provide new results in the problem of local uniformization in positive characteristic. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
Articles published in other media outlets (0 total):
More itemsLess items

Scientific publications (11)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CUTKOSKY, STEVEN DALE; NOVACOSKI, JOSNEI. Essentially finite generation of valuation rings in terms of classical invariants. Mathematische Nachrichten, v. 294, n. 1, p. 15-37, . (17/17835-9)
BARNABE, M. S.; NOVACOSKI, J.; SPIVAKOVSKY, M.. On the structure of the graded algebra associated to a valuation. Journal of Algebra, v. 560, p. 667-679, . (17/17835-9)
BARNABE, MATHEUS DOS SANTOS; NOVACOSKI, JOSNEI. Valuations on K[x] approaching a fixed irreducible polynomial. Journal of Algebra, v. 592, p. 100-117, . (17/17835-9)
DE MORAES, MICHAEL; NOVACOSKI, JOSNEI. Limit key polynomials as p-polynomials. Journal of Algebra, v. 579, p. 22-pg., . (17/17835-9)
NOVACOSKI, JOSNEI. Key polynomials and minimal pairs. Journal of Algebra, v. 523, p. 1-14, . (17/17835-9, 15/23409-7)
NOVACOSKI, JOSNEI. On MacLane-Vaquie key polynomials. Journal of Pure and Applied Algebra, v. 225, n. 8, . (17/17835-9)
DE MORAES, MICHAEL; NOVACOSKI, JOSNEI. Perron transforms and Hironaka's game. Journal of Algebra, v. 563, p. 100-110, . (17/17835-9)
NOVACOSKI, J. A.; SILVA DE SOUZA, C. H.. On truncations of valuations. Journal of Pure and Applied Algebra, v. 226, n. 6, . (17/17835-9, 20/05148-0)
NART, ENRIC; NOVACOSKI, JOSNEI. The defect formula. ADVANCES IN MATHEMATICS, v. 428, p. 44-pg., . (21/11246-7, 17/17835-9)
NART, ENRIC; NOVACOSKI, JOSNEI. Geometric parametrization of valuations on a polynomial ring in one variable. MATHEMATISCHE ZEITSCHRIFT, v. 304, n. 4, p. 21-pg., . (21/11246-7, 17/17835-9)
KUHLMANN, FRANZ-VIKTOR. Valued fields with finitely many defect extensions of prime degree. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 21, n. 03, p. 18-pg., . (17/17835-9)

Please report errors in scientific publications list by writing to: