arXiv subjects

Carlos Tejero Prieto

Publications and source records attributed to Carlos Tejero Prieto.

14 recordsLinked to original sources

arXiv2022

The meaning of the Sky of Salamanca

After presenting the main characteristics of the Sky of Salamanca, we analyse whether what is represented in it is motivated by astrological or astronomical considerations. We will see that the astrological explanation based on the system of planetary houses described in Claudius Ptolemy's Tetrabiblos does not correspond to the planetary configuration we see in the salmantine vault. Finally, we will conclude that the astronomical interpretation of the Sky of Salamanca is justified by the representation of the Universe known in the 15th century according to the Almagest, by the placement of the stars in the constellations according to that work and by the dating of the painted planetary configuration, which circumstantial evidence places in August 1475.

physics.hist-ph↗

arXiv2022

Astronomy at the University of Salamanca at the end of the 15th century. What "El Cielo de Salamanca" tells us

"El Cielo de Salamanca" ("The Sky of Salamanca") is a quarter-sphere-shaped vault 8.70 metres in diameter. It was painted sometime between 1480 and 1493 and shows five zodiacal constellations, three boreal and six austral. The Sun and Mercury are also represented. It formed part of a three times larger vault depicting the 48 Ptolemaic constellations and the rest of the planets known at the time. This was a splendid work of art that covered the ceiling of the first library of the University of Salamanca, one of the oldest in Europe having obtained its royal charter in 1218. But it was also a pioneering scientific work: a planetarium used to teach astronomy, the first of its kind in the history of Astronomy that has come down to us in the preserved part that we now call "The Sky of Salamanca". We describe the scientific context surrounding the chair of Astrology founded around 1460 at the University of Salamanca, which led to the production of this unique scientific work of art and to the flourishing of Astronomy in Salamanca. We analyse the possible dates compatible with it, showing that they are extremely infrequent. In the period of 1100 years from 1200 to 2300 that we studied there are only 23 years that have feasible days. We conclude that the information contained in "El Cielo de Salamanca" is not sufficient to assign it to a specific date but rather to an interval of several days that circumstantial evidence seems to place in August 1475. The same configuration of the sky will be observable, for the first time in 141 years, from the 22nd to the 25th of August 2022. The next occasion to observe it live will be in 2060.

physics.hist-ph↗

arXiv2019

Lie subalgebras of Differential Operators in one Variable

Let $\operatorname{Witt}$ be the Lie algebra generated by the set $\{L_i\,\vert\, i \in {\mathbb Z}\}$ and $\operatorname{Vir}$ its universal central extension. Let $\operatorname{Diff}(V)$ be the Lie algebra of differential operators on $V=\mathbb{C}[[z]]$, $\mathbb{C}((z))$ or $V=\mathbb{C}(z)$. We explicitly describe all Lie algebra homomorphisms from $\mathfrak{sl}(2)$, $\operatorname{Witt}$ and $\operatorname{Vir}$ to $\operatorname{Diff}(V)$ such that $L_0$ acts on $V$ as a first order differential operator.

math.RT↗

arXiv2017

Derived equivalences of Abelian varieties and symplectic isomorphisms

We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by Orlov, which maps equivalences to symplectic isomorphisms, is surjective.

math.AG↗

arXiv2017

Derived equivalences and Kodaira fibers

We give necessary conditions for two (including non-reduced and multiple) Kodaira curves to be derived equivalent. We classify Fourier-Mukai partners of any reduced Kodaira curve. We prove that the derived category of singularities of any non-reduced and non-multiple Kodaira curve is idempotent complete.

math.AG↗

arXiv2016

Natural operations on holomorphic forms

We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence {\it à la Galois}.

math.CV↗

arXiv2016

The geometry of real reducible polarizations in quantum mechanics

The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle. The existence of reducible quantum structures leads to considering the class of Liouville symplectic manifolds. Our main application of this modified geometric quantization scheme is to Quantum Mechanics on Riemannian manifolds. With this method we obtain an energy operator without the scalar curvature term that appears in the standard formulation, thus agreeing with the usual expression found in the Physics literature.

math-ph↗

arXiv2016

Construction of simple non-weight sl(2)-modules of arbitrary rank

We study simple non-weight ${\mathfrak{sl}}(2)$-modules which are finitely generated as ${\mathbb C}[z]$-modules. We show that they are described in terms of semilinear endomorphisms and prove that the Smith type induces a stratification on the set of these ${\mathfrak{sl}}(2)$-modules, providing thus new invariants. Moreover, we show that there is a notion of duality for these type of ${\mathfrak{sl}}(2)$-modules. Finally, we show that there are simple non-weight ${\mathfrak{sl}}(2)$-modules of arbitrary rank by constructing a whole new family of them.

math.RT↗

arXiv2016

Virasoro and KdV

We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the differential operators defined by the Virasoro conjecture and obtain some factorization properties of the solutions as well as a link to the multicomponent KP hierarchy.

math.RT↗

arXiv2014

On the geometry of the energy operator in quantum mechanics

We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.

math-ph↗

arXiv2012

Relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations

We study the group of relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano or anti-Fano fibrations. For Weierstrass and Fano or anti-Fano fibrations we are able to describe this group completely. For abelian schemes over an arbitrary base we prove that if two of them are relative Fourier-Mukai partners then there is an isometric isomorphism between the fibre products of each of them and its dual abelian scheme. If the base is normal and the slope map is surjective we show that these two conditions are equivalent. Moreover in this situation we completely determine the group of relative Fourier-Mukai transforms and we prove that the number of relative Fourier-Mukai partners of a given abelian scheme over a normal base is finite.

math.AG↗

arXiv2009

Moduli Spaces of Semistable Sheaves on Singular Genus One Curves

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli spaces of semistable sheaves on the curve. For rank zero, the moduli spaces are symmetric powers of the curve whilst for a fixed positive rank there are only a finite number of non-isomorphic spaces. We prove similar results for the relative semistable moduli spaces on an arbitrary genus one fibration with no conditions either on the base or on the total space. For a cycle $E_N$ of projective lines, we show that the unique degree 0 stable sheaves are the line bundles having degree 0 on every irreducible component and the sheaves $\mathcal{O}(-1)$ supported on one irreducible component. We also prove that the connected component of the moduli space that contains vector bundles of rank $r$ is isomorphic to the $r$-th symmetric product of the rational curve with one node.

math.AG↗

arXiv2007

Fourier-Mukai transforms for coherent systems on elliptic curves

We determine all the Fourier-Mukai transforms for coherent systems consisting of a vector bundle over an elliptic curve and a subspace of its global sections, showing that these transforms are indexed by the positive integers. We prove that the natural stability condition for coherent systems, which depends on a parameter, is preserved by these transforms for small and large values of the parameter. By means of the Fourier-Mukai transforms we prove that certain moduli spaces of coherent systems corresponding to small and large values of the parameter are isomorphic. Using these results we draw some conclusions about the possible birational type of the moduli spaces. We prove that for a given degree $d$ of the vector bundle and a given dimension of the subspace of its global sections there are at most $d$ different possible birational types for the moduli spaces.

math.AG↗

arXiv2004

Fourier-Mukai and Nahm transforms for holomorphic triples on elliptic curves

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple -- vortices -- and explore some of its basic properties. Our approach combines direct methods with dimensional reduction techniques, relating triples over a curve with vector bundles over the product of the curve with the complex projective line.

math.AG↗