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Thaís M. Dalbelo

Publications and source records attributed to Thaís M. Dalbelo.

5 recordsLinked to original sources
arXiv2026

The Euler characteristic of Milnor fibers over 2-generic symmetric determinantal varieties

In this work we present a formula for the Euler characteristic of the Milnor fiber of non-degenerate functions $f: X \to \mathbb{C}$ with isolated critical set relative to a stratification, where $X$ is a $2$-generic symmetric determinantal variety. The formula is obtained in two steps. Firstly, we explicitly describe the toric structure of those varieties. Secondly, we compute volumes of Newton polyhedra arising from the toric structure. The result then follows from Matsui-Takeuchi's formula for Milnor fibers over toric varieties. As an application, we compute the local Euler obstruction of $X$ at the origin and the local Euler obstruction of $f$. We also relate the Euler obstruction of $f$ to the Milnor number of a certain polynomial associated to $f$.

math.AG↗
arXiv2025

Newton polyhedra and the integral closure of ideals on toric varieties

In this work, we extend Saia's results on the characterization of Newton non-degenerate ideals to the context of ideals in $O_{X(S)}$, where $X(S)$ is an affine toric variety defined by the semigroup $S\subset \mathbb{Z}^{n}_{+}$. We explore the relationship between the integral closure of ideals and the Newton polyhedron. We introduce and characterize non-degenerate ideals, showing that their integral closure is generated by specific monomials related to the Newton polyhedron.

math.AG↗
arXiv2025

Nash blowups of 2-generic determinantal varieties in positive characteristic

We show that the Nash blowup of 2-generic determinantal varieties over fields of positive characteristic is non-singular. We prove this in two steps. Firstly, we explicitly describe the toric structure of such varieties. Secondly, we show that in this case the combinatorics of Nash blowups are free of characteristic. The result then follows from the analogous result in characteristic zero proved by W. Ebeling and S. M. Gusein-Zade.

math.AG↗
arXiv2025

Stratified Morse critical points and Brasselet number on non-degenerate locally tame singularities

The generalization of the Morse theory presented by Goresky and MacPherson is a landmark that divided completely the topological and geo\-me\-tri\-cal study of singular spaces. Let \{$X_t\}_t$ be a suitable family of germs at $0$ of complete intersection varieties in $\mathbb{C}^n$ and $\{f_t\}_t, \{g_t\}_t$ families of non-constant polynomial functions on $X_t$. If the germs $X_t$, $X_t \cap f_t^{-1}(0)$ and $X_t\cap f_t^{-1}(0) \cap g_t^{-1}(0)$ are non-degenerate, locally tame, complete intersection varieties, for each $t,$ we prove that the difference of the Brasselet numbers, ${\rm B}_{f_t,X_t}(0)$ and ${\rm B}_{f_t,X_t\cap g_t^{-1}(0)}(0)$, is related with the number of Morse critical points {on the regular part of the Milnor fiber} of $f_t$ appearing in a morsefication of $g_t$, even in the case where $g_t$ has a critical locus with arbitrary dimension. This result connects topological and geometric properties and allows us to determine some interesting formulae, mainly in terms of the combinatorial information from Newton polyhedra.

math.GT↗