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V. Muñoz

Publications and source records attributed to V. Muñoz.

10 recordsLinked to original sources
arXiv2020

Negative Sasakian structures on simply-connected 5-manifolds

We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form $\#_k(S^2\times S^3)$. First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [BG], of determining which simply connected rational homology spheres admit both negative and positive Sasakian structures. Second, we prove that the connected sum $\#_k(S^2\times S^3)$ admits negative quasi-regular Sasakian structures for any $k$. This yields a complete answer to another question posed in [BG].

math.DG↗
arXiv2020

Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds

Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Kollár). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic Kähler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with $b_1=0$ and $b_2>1$ there cannot be $b_2$ smooth disjoint complex curves of genus g>0 spanning the (rational) homology.

math.DG↗
arXiv2013

Equivariant vector bundles and logarithmic connections on toric varieties

Let X be a smooth complete complex toric variety such that the boundary is a simple normal crossing divisor, and let E be a holomorphic vector bundle on X. We prove that E admits an equivariant structure if and only if E admits a logarithmic connection singular over D. More precisely, we show that an equivariant vector bundle on X has a tautological integrable logarithmic connection singular over D. This is used in computing the Chern classes of the equivariant vector bundles on X. We also prove a version of the result for holomorphic vector bundles on log parallelizable G-pairs (X,D), where G is a simply connected complex affine algebraic group.

math.AG↗
arXiv2007

Hodge polynomials of the moduli spaces of triples of rank (2,2)

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic triple $(E_1,E_2,ϕ)$ on $X$ consists of two holomorphic vector bundles $E_{1}$ and $E_{2}$ over $X$ and a holomorphic map $ϕ\colon E_{2} \to E_{1}$. There is a concept of stability for triples which depends on a real parameter $σ$. In this paper, we determine the Hodge polynomials of the moduli spaces of $σ$-stable triples with $\mathrm{rk}(E_1)=\mathrm{rk}(E_2)=2$, using the theory of mixed Hodge structures (in the cases that they are smooth and compact). This gives in particular the Poincar{é} polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.

math.AG↗
arXiv2006

Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,ϕ)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $ϕ\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.

math.AG↗
arXiv2006

On the geometry of moduli spaces of coherent systems on algebraic curves

Let $C$ be an algebraic curve of genus $g$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $α$. We study the geometry of the moduli space of coherent systems for different values of $α$ when $k\leq n$ and the variation of the moduli spaces when we vary $α$. As a consequence, for sufficiently large $α$, we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case $k=n-1$ explicitly, and give the Poincaré polynomials for the case $k=n-2$.

math.AG↗
arXiv2005

Betti numbers of the moduli space of rank 3 parabolic Higgs bundles

We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and we study their variation with this parameter.

math.AG↗
arXiv1996

Investigation of conduction band structure, electron scattering mechanisms and phase transitions in indium selenide by means of transport measurements under pressure

In this work we report on Hall effect, resistivity and thermopower measurements in n-type indium selenide at room temperature under either hydrostatic and quasi-hydrostatic pressure. Up to 40 kbar (= 4 GPa), the decrease of carrier concentration as the pressure increases is explained through the existence of a subsidiary minimum in the conduction band. This minimum shifts towards lower energies under pressure, with a pressure coefficient of about -105 meV/GPa, and its related impurity level traps electrons as it reaches the band gap and approaches the Fermi level. The pressure value at which the electron trapping starts is shown to depend on the electron concentration at ambient pressure and the dimensionality of the electron gas. At low pressures the electron mobility increases under pressure for both 3D and 2D electrons, the increase rate being higher for 2D electrons, which is shown to be coherent with previous scattering mechanisms models. The phase transition from the semiconductor layered phase to the metallic sodium cloride phase is observed as a drop in resistivity around 105 kbar, but above 40 kbar a sharp nonreversible increase of the carrier concentration is observed, which is attributed to the formation of donor defects as precursors of the phase transition.

cond-mat↗