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Browsing by Author "Fernández Fernández, María Cruz"
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Abanicos de Groebner e ideales tóricos [Final Degree Work]
Fernández Antúnez, Fátima (201606)The Groebner fan of a polynomial ideal was originally introduced by T. Mora and L. Robbiano in 1988. In this Bachelor’s Degree Final Project we study the Groebner fan of a polynomial ideal, including the proof by Fukuda, ...

Exponential growth of rank jumps for Ahypergeometric systems [Article]
Fernández Fernández, María Cruz (European Mathematical Society, 2013)The dimension of the space of holomorphic solutions at nonsingular points (also called the holonomic rank) of a A–hypergeometric system MA(β) is known to be bounded above by 22d vol(A) [SST00], where d is the rank of ...

Gevrey solutions of irregular hypergeometric systems in two variables [Article]
Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (Elsevier, 20110801)We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with ...

Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve [Article]
Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (American Mathematical Society, 2011)We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect ...

Irregular hypergeometric Dmodules [Article]
Fernández Fernández, María Cruz (E, 20100801)We study the irregularity of hypergeometric Dmodules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the ...

Irregular modified AHypergeometric systems [Article]
Castro Jiménez, Francisco Jesús; Fernández Fernández, María Cruz; Koike, Tatsuya; Takayama, Nobuki (American Mathematical Society, 2015)A modified Ahypergeometric system is a system of differential equations for the function f(t w · x) where f(y) is a solution of an Ahypergeometric system in n variables and w is an n dimensional integer vector, which is ...

On irregular binomial Dmodules [Article]
Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (Springer, 201212)We prove that a holonomic binomial D–module MA(I, β) is regular if and only if certain associated primes of I determined by the parameter vector β ∈ Cd are homogeneous. We further describe the slopes of MA(I, β) along a ...

Restriction of hypergeometric Dmodules with respect to coordinate subspaces [Article]
Fernández Fernández, María Cruz; Walther, Uli (American Mathematical Society, 2011)We compute the restriction of an Ahypergeometric Dmodule with respect to a coordinate subspace under certain genericity conditions on the parameter.

Soluciones Gevrey de sistemas hipergeométricos [PhD Thesis]
Fernández Fernández, María Cruz (2010)Esta memoria versa sobre la irregularidad de los Dmódulos hipergeométricos MA(β)(cf. Definición 3.1.3), introducidos p or Gelfand, Graev, Kapranov y Zelevinsky [GGZ87], [GZK89]. Nuestro estudio se basa principalmente en ...