Marta Aldasorok bere tesia defendatuko du asteartean, ekainak 9

Defentsa Zientzia eta Teknologia Fakultateko (EHU - Leioa) 1.A1 gelan egingo da, 16:30ean.

Marta Aldasoro Rosales Matematikan graduatu zen Euskal Herriko Unibertsitatean (2015-2019), eta, ondoren, Matematika Aurreratuetako Masterra lortu zuen Madrilgo Unibertsitate Konplutentsean (2019-2020). 2021eko urtarrilean doktoretza hasi zuen Javier Fernández de Bobadillak gainbegiratuta, Fisika Matematikoko taldean, BCAMeko STAG arloan. Ikasturte honetako irailetik, Zaragozako Unibertsitatean dago irakasle eta ikertzaileen kontratu batekin, Jorge Martín Moralesekin batera lanean.

“Deformations of $\mu $– constant Surface Singularities and the A 'Campo Space in Logarithmic Geometry” izeneko tesia Javier Fernández de Bobadilla irakasleak zuzendu du (BCAM & Ikerbasque). Defentsa 2026ko ekainaren 9rako programatuta dago, Zientzia eta Teknologia Fakultateko (EHU - Leioa) 1.A1 gelan, 16:30ean.

BCAMeko kide guztien izenean, etorkizunerako onena opa diougu, bai arlo profesionalean, bai pertsonalean.

Abstract

We summarize the main results of this thesis.

For the first result, we work with a 1-parameter family σ : X →∆ of isolated hypersurface singularities of fibre dimension 2. We show that if the Milnor number is constant, then any semistable model, obtained from σ after a sufficiently large base change must satisfy nontrivial restrictions. These restrictions are in terms of the dual complex, Hodge structure and numerical invariants of the central fibre. To achieve this, we make use of the Steenbrink spectral sequence degenerating to the cohomology of a generic fibre of the resolution, endowed with the limit mixed Hodge structure.

In the second part of the thesis, we extend the classical A’Campo space to the setting of fine log analytic spaces. We associate the A’Campo space to a fine log analytic space, whose ghost sheaf is quasi-constructible with respect to a finite trivializing stratification, and show that this construction is compatible with exact and vertical morphisms that admit coverings by good charts. More precisely, we obtain a functor from a suitable category of fine log analytic spaces to the category of topological manifolds with boundary and continuous maps.

Furthermore, under a natural transversality condition on the associated sharp cone, the local A’Campo space of a fine monoid carries a smooth structure obtained by pulling back the free-monoid model of Fernández de Bobadilla and Pełka, and this smooth structure is compatible with the topological structure introduced here.