Reports de recerca
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The singular Weinstein conjecture
(2020-06-04)
External research report
Open AccessIn this article, we investigate Reeb dynamics on $b^m$-contact manifolds, previously introduced in \cite{MO}, which are contact away from a hypersurface $Z$ but satisfy certain transversality conditions on $Z$. The study ... -
A b-symplectic slice theorem
(2020-09)
External research report
Open AccessIn this article, motivated by the study of symplectic structures on manifolds with bound-ary and the systematic study ofb-symplectic manifolds started in [10], we prove a slice theorem forLie group actions onb-symplectic manifolds -
The geometry and topology of contact structures with singularities
(2020-05-20)
External research report
Open AccessIn this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. ... -
Bernstein's inequality and holonomicity for certain singular rings
(2021)
External research report
Open AccessIn this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded ... -
Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
(2019)
External research report
Open AccessThis paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of ... -
Poincaré series of multiplier and test ideals
(2021)
External research report
Open AccessWe prove the rationality of the Poincaré series of multiplier ideals in any dimension and thus extending the main results for surfaces of Galindo and Monserrat and Alberich-Carramiñana et al. Our results also hold for ... -
Bass numbers of local cohomology of cover ideals of graphs
(2019)
External research report
Open AccessWe develop splitting techniques to study Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally we are ... -
Local cohomology of binomial edge ideals and their generic ideals
(2019)
External research report
Open AccessWe provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford ... -
A surprising fact about D-modules in characteristic p>0
(2004)
External research report
Open AccessLet R = k[x1, . . . , xd] be the polynomial ring in d independent variables, where k is a field of characteristic p > 0. Let DR be the ring of k-linear differential operators of R and let f be a polynomial in R. In this ... -
Divisors of expected Jacobian type
(2020)
External research report
Open AccessDivisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of D-modules. In this work we are interested on divisors of expected Jacobian type, that ... -
Rigidity of cotangent lifts and integrable systems
(2020-05)
External research report
Open AccessIn this article we generalize a theorem by Palais on the rigidity ofcompact group actions to cotangent lifts. We use this result to prove rigidity forintegrable systems on symplectic manifolds including sytems with ... -
b-Structures on Lie groups and Poisson reduction
(2020-09)
External research report
Open AccessWe introduce the notion of b-Lie group as a pair(G, H) where Gis a Lie group and H is a codimension-one Lie subgroup, and study the associated canonical b-symplectic structure on the b-cotangent bundle bT*G together with ...
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