The modularity of the Barth-Nieto quintic and its relatives

The moduli space of (1,3)-polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth-Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y, respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L-function of their common third \'etale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group \Gamma_1(6). By Tate's conjecture, this should imply that Y, the fibred square of the universal elliptic curve S_1(6), and Verrill's rigid Calabi-Yau Z_{A_3}, which all have the same L-function, are in correspondence over Q. We show that this is indeed the case by giving explicit maps.Comment: 30 pages, Latex2

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

Age-dependent changes in geometry, tissue composition and mechanical properties of fetal to adult cryopreserved human heart valves

Copyrigh

The F-BAR protein pacsin2 inhibits asymmetric VE-cadherin internalization from tensile adherens junctions

Vascular homoeostasis, development and disease critically depend on the regulation of endothelial cell-cell junctions. Here we uncover a new role for the F-BAR protein pacsin2 in the control of VE-cadherin-based endothelial adhesion. Pacsin2 concentrates at focal adherens junctions (FAJs) that are experiencing unbalanced actomyosin-based pulling. FAJs move in response to differences in local cytoskeletal geometry and pacsin2 is recruited consistently to the trailing end of fast-moving FAJs via a mechanism that requires an intact F-BAR domain. Photoconversion, photobleaching, immunofluorescence and super-resolution microscopy reveal polarized dynamics, and organization of junctional proteins between the front of FAJs and their trailing ends. Interestingly, pacsin2 recruitment inhibits internalization of the VE-cadherin complex from FAJ trailing ends and is important for endothelial monolayer integrity. Together, these findings reveal a novel junction protective mechanism during polarized trafficking of VE-cadherin, which supports barrier maintenance within dynamic endothelial tissue

A new geometric description for Igusa's modular form (azy)5(azy)_5

The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different description for this modular form is provided by resorting to a peculiar geometrical approach.Comment: 10 page

The F-BAR protein pacsin2 inhibits asymmetric VE-cadherin internalization from tensile adherens junctions

Vascular homoeostasis, development and disease critically depend on the regulation of endothelial cell-cell junctions. Here we uncover a new role for the F-BAR protein pacsin2 in the control of VE-cadherin-based endothelial adhesion. Pacsin2 concentrates at focal adherens junctions (FAJs) that are experiencing unbalanced actomyosin-based pulling. FAJs move in response to differences in local cytoskeletal geometry and pacsin2 is recruited consistently to the trailing end of fast-moving FAJs via a mechanism that requires an intact F-BAR domain. Photoconversion, photobleaching, immunofluorescence and super-resolution microscopy reveal polarized dynamics, and organization of junctional proteins between the front of FAJs and their trailing ends. Interestingly, pacsin2 recruitment inhibits internalization of the VE-cadherin complex from FAJ trailing ends and is important for endothelial monolayer integrity. Together, these findings reveal a novel junction protective mechanism during polarized trafficking of VE-cadherin, which supports barrier maintenance within dynamic endothelial tissue