E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

Sintaxis del discurso en Dt 4, 1-40

Dt 4, 1-40 it a Biblical text particularly relevant, both for its location and sense within the Deuteronomy book, as well as for its relation with the overall Deuteronomist literature. However, we do not handle in-depth and extensive studies of this text, with exception of the works published by G. Braulik516, D. Knapp517 and K. Holter518, and other exploratory studies much thoroughly investigated, as well as small monographic ones specified in a particular matter. On the other hand, the investigation of the text has been focused mainly around the historical and theological analysis of it, with the purpose to determine the time in which the text was introduced in the total of the book, as well as to weight the significance of the different stratum of the text, its sources... For this reason, other medium of approach to the text has been left aside, or had been used only as instruments to be served to the main purpose of this study. This has been for instance the study of the literary analysis. Nevertheless, during these last years, the literary investigation of the biblical texts (linguistics, narrative, rhetoric, comparative literature...) has gained boom, and had allowed a great appreciation of these texts, overall its historical or theological relevance. Dt 4, 1-40 has been benefit from all of it. The studies dedicated to the literary analysis of Dt 4, 1-40 show considerable patterns on the ways they had been carried. We have analysed them from the syntax and narrative points of view, fields very little investigated up to now. We believe it is necessary to study the text from these two perspectives to appreciate the wealth of this literary composition beyond the topics covered on it, and to contribute this way to a deep investigation of such a significant text in shape and content for the present Biblical Philology. The final objective of our study it is to arrive to a full comprehension of the thematic and literary unity of the text through its syntactic and narrative analysis, and, at the same time, to determine the mutual and necessary relationship that exist between one to another in this line of investigation...