A rigid Calabi--Yau 3-fold

The aim of this paper is to analyze some geometric properties of the rigid Calabi--Yau threefold $\mathcal{Z}$ obtained by a quotient of $E^3$, where $E$ is a specific elliptic curve. We describe the cohomology of $\mathcal{Z}$ and give a simple formula for the trilinear form on $Pic(\mathcal{Z})$. We describe some projective models of $\mathcal{Z}$ and relate these to its generalized mirror. A smoothing of a singular model is a Calabi--Yau threefold with small Hodge numbers which was not known before.Comment: 24 pages, Version 2: minor changes, references adde

Orbital degeneracy loci and applications

Degeneracy loci of morphisms between vector bundles have been used in a wide variety of situations. We introduce a vast generalization of this notion, based on orbit closures of algebraic groups in their linear representations. A preferred class of our orbital degeneracy loci is characterized by a certain crepancy condition on the orbit closure, that allows to get some control on the canonical sheaf. This condition is fulfilled for Richardson nilpotent orbits, and also for partially decomposable skew-symmetric three-forms in six variables. In order to illustrate the efficiency and flexibility of our methods, we construct in both situations many Calabi--Yau manifolds of dimension three and four, as well as a few Fano varieties, including some new Fano fourfolds.Comment: To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5

Scattering diagrams and Jeffrey-Kirwan residues

We show that the consistent completion of an initial scattering diagram in $M_{\mathbb{R}}$ (for a finite rank lattice $M$) can be expressed quite generally in terms of the Jeffrey-Kirwan residues of certain explicit meromorphic forms, by using the Maurer-Cartan asymptotic analysis developed by Chan-Leung-Ma and Leung-Ma-Young. A similar result holds for the associated theta functions.Comment: Fixed a referenc

Mapping free resolutions of length three II -- Module formats

Let $M$ be a perfect module of projective dimension 3 in a Gorenstein, local or graded ring $R$. We denote by \FF the minimal free resolution of $M$. Using the generic ring associated to the format of \FF we define higher structure maps, according to the theory developed by Weyman in "Generic free resolutions and root systems" (Annales de l'Institut Fourier} 68.3 (2018), pp. 1241--1296). We introduce a generalization of classical linkage for $R$-module using the Buchsbaum--Rim complex, and study the behaviour of structure maps under this Buchsbaum--Rim linkage. In particular, for certain formats we obtain criteria for these $R$-modules to lie in the Buchsbaum--Rim linkage class of a Buchsbaum--Rim complex of length 3.Comment: 30 page

Transfected poly(I:C) activates different dsRNA receptors leading to apoptosis or immunoadjuvant response in androgen-independent prostate cancer cells

Background: Castration-resistant prostate cancer (CRPC) is refractory to chemo-radiotherapy. Results: Transfection of the synthetic analog of dsRNA poly(I:C) simultaneously stimulates apoptosis and IFN- expression through different pathways in androgen-independent prostate cancer (PCa) cells. Conclusion: Dual parallel pathways triggered by distinct receptors activate direct and immunologically mediated antitumor effects in advanced PCa. Significance: The proapoptotic/immunoadjuvant poly(I:C)-Lipofectamine complex may offer new therapeutic insights into CRPC

TBA type equations and tropical curves

The Joyce integrable system and the corresponding Bridgeland\u2013Toledano-Laredo connections are fundamental objects associated with suitable abelian categories or, more generally, with a class of continuous families of stability data. We offer an overview of some of our work, mostly joint with M. Garcia Fernandez, focusing on equations of TBA type as a useful tool in the analysis of these objects and their deformations, and as a means to establish a connection with tropical geometry. \ua9 2016 World Scientific Publishing Company

TNF-α inhibits GDNF levels in Sertoli cells, through a NF-κB-dependent, HES1-dependent mechanism

Glial cell line-derived neurotrophic factor (GDNF) is a soluble molecule crucial for the regulation of the spermatogonial stem cells (SSC) of the testis. The effects of GDNF on target cells have been extensively described, but mechanisms underlying GDNF regulation are currently under investigation. In the nervous system, GDNF expression is regulated by pro-inflammatory cytokines including lipopolysaccharide (LPS), interleukin 1 beta (IL-1β), and tumor necrosis factor alpha (TNF-α) but the effect of these cytokines on GDNF expression in the testis is unclear