The Picard group of the moduli stack of stable hyperelliptic curves

We compute the Picard group of the moduli stack of stable hyperelliptic curves of any genus, exhibiting explicit and geometrically meaningful generators and relations.Comment: 6 pages, LaTeX; corrected minor errors, added reference

Teichmueller space via Kuranishi families

We construct Teichmueller space by patching together Kuranishi families. We also discuss the basic properties of Teichmueller space, and in particular show that our construction leads to simplifications in the proof of Teichmueller's theorem asserting that the genus g Teichmueller space is homeomorphic to a (6g-6)-dimensional ball.Comment: 26 pages; minor mistakes corrected, references added and correcte

Moduli of roots of line bundles on curves

We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on nodal curves as boundary points, are carried out and compared with pre-existing ones.Comment: Final version, added references. To appear in Trans. Amer. Math. So

Addendum 7.1.1981. Correzione a "su una congettura di Petri"

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Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Exploring the hidden riches: Recent remarkable faunistic records and range extensions in the bee fauna of Italy (Hymenoptera, Apoidea, Anthophila)

The area sourrounding the Mediterranean basin is recognised as a major biodiversity hotspot for bees, and Italy is amongst the European countries with the highest bee species richness. Detailed knowledge of bee distribution is crucial for understanding bee biology and designing tailored conservation strategies, but is still insufficient in southern European countries, especially in Italy.We report recent finds of 48 bee species that yield significant novelties for the Italian bee fauna. Eight species, namely Andrena confinis Stöckhert, Anthidiellum breviusculum Pérez, Coelioxys alatus Foerster, Lasioglossum algericolellum Strand, Megachile lapponica Thomson, Megachile opacifrons Pérez, Megachile semicircularis auct. nec Zanden and Trachusa integra Eversmann are reported as new for Italy. In addition, Andrena binominata Smith, Andrena compta Lepeletier, Colletes acutus Pérez, Lasioglossum strictifrons Vachal, Rhodanthidium siculum Spinola and Rhodanthidium sticticum Fabricius are newly recorded from mainland Italy, Osmia heteracantha Pérez from Sardegna and Nomada flavopicta Kirby from Sicilia. We also report significant range extensions for other bee species and recent records of species that had long gone unrecorded in Italy. The combination of morphology and DNA barcoding provided reliable identifications even for the most challenging specimens. As several of our records come from areas neglected by bee experts in the past, this study stands out as a key indicator of a bee faunistic richness still awaiting discovery and hopefully it will stimulate the interest of taxonomists and stakeholders in pursuing bee research in Italy in the near future

Analisi, Algebra, Geometria

TesisLima NorteEscuela de EducaciónDidáctica y Evaluación de los AprendizajesLa investigación que se presenta a continuación tuvo como objetivo determinar el nivel de uso de las tecnologías de la información y comunicación en los docentes del nivel secundaria del distrito de Rioja, 2018. La tesis presenta un enfoque cuantitativo, con un corte transversal, con un nivel descriptivo simple y un diseño no experimental. Para su realización, se aplicó la técnica de la encuesta utilizando como instrumento un Cuestionario a una muestra de 79 docentes del nivel secundaria del distrito de Rioja, dicha muestra se obtuvo mediante la técnica de muestreo probabilístico estratificado por áreas curriculares. Por ser un estudio descriptivo simple no se contó con hipótesis de trabajo. Los resultados revelaron que el nivel de uso de las tecnologías de la información y comunicación en los docentes es alto en un 69,6%, muy alto en un 26,5% y medio en un 3,8%. Asimismo, se muestra, que el 50% de los docentes tienen un nivel alto máximo (43 puntos) y el 50% restante, supera dicho nivel. El promedio de nivel de uso es 43.86±4.83, con un bajo grado de variación (11.01%). Concluyendo que la mayoría de docentes han logrado el nivel alto en el uso de las TIC tanto en su labor docente como en el fomento de su uso entre los estudiantes