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.Comment: 78 pages. Extended version. Added a section with the fixed determinant case. To appear in Memoirs of the AM

El lesbianismo como monstruosidad en El cumpleaños de Alicia de Henry Díaz Vargas

This play enacts the celebration of a birthday party, which is dramatized following the cyclic and regenerative characteristics of the carnivalesque. The play is also based on the eternal struggle between thanatos and eros, proper of an erotic relationship, which, in this lesbian play, impels the lovers to kill each other. Lesbianism is a way of life that liberates women from patriarchal order. However, in Díaz’s play, the lesbian relationship is conceived as a monstrosity, as oppressive as the worse heterosexual relationship. My contention is that Díaz constructs female characters based on deforming fologocentric stereotypes that destine to death those who dare to stand outside the norm. (WOM, in Spanish

Luis Ramiro Beltrán: El apocalipsis de la humanidad en El cofre de Selenio

This article studies El cofre de Selenio, a postmodern play by the Bolivian playwright Luis Ramiro Beltrán. The play is an allegorical search for the light, for the meaning of life, but it is also a discourse for world peace, a statement that denounces the hegemonic ideologies that have oppressed men throughout history, a rejection of the war technology, of the sciences that make possible an apocalyptic nuclear hecatomb. An intercultural plurality contributes to the universality of its aim, however, the referents, though fragmented and plural, they are localized and historically specific. The play itself does not have a plot, in the conventional sense of the term, but the events take place in a synchronic time, in a multispatial place, where thirty-two characters from throughout history interact. (WOM, in Spanish

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 $\alpha$. We study the geometry of the moduli space of coherent systems for different values of $\alpha$ when $k\leq n$ and the variation of the moduli spaces when we vary $\alpha$. As a consequence, for sufficiently large $\alpha$, 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 Poincar\'e polynomials for the case $k=n-2$.Comment: 38 pages; v3. Appendix and new references added; v4. minor corrections, two added references; v5. final version, one typo corrected and one reference delete