Search results for "Moduli"

A combinatorial algorithm related to the geometry of the moduli space of pointed curves

2002

As pointed out in Arbarello and Cornalba ( J. Alg. Geom. 5 (1996), 705–749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193–219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be determined by the algorithm we introduce in this paper.

Aging and chronic inflammation: highlights from a multidisciplinary workshop

2023

Abstract: Aging is a gradual, continuous series of natural changes in biological, physiological, immunological, environmental, psychological, behavioral, and social processes. Aging entails changes in the immune system characterized by a decrease in thymic output of naïve lymphocytes, an accumulated chronic antigenic stress notably caused by chronic infections such as cytomegalovirus (CMV), and immune cell senescence with acquisition of an inflammatory senescence-associated secretory phenotype (SASP). For this reason, and due to the SASP originating from other tissues, aging is commonly accompanied by low-grade chronic inflammation, termed “inflammaging”. After decades of accumulating evide…

The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense

2014

Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good family for $\mathcal{M}_{n,2n+2}$ is Zariski dense in the corresponding symplectic or orthogonal group if $n\geq 3$. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever $n\geq 3$. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of $m$ ordered points in $\mathbb{P}^n$ is shown to be large once it is not…

On the geometry of S2

2009

We investigate topological properties of the moduli space of spin structures over genus two curves. In particular, we provide a combinatorial description of this space and give a presentation of the (rational) cohomology ring via generators and relations.

2021

Abstract We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is to study log structures that are incoherent on a subspace of codimension 2 and prove a Hodge–de Rham degeneration theorem for such log spaces that also settles a conjecture by Danilov. We show that the homotopy equivalence between Maurer–Cartan solutions and deformations combined with Batalin–Vilkovisky theory can be used to obtain smoothings. The construction of new Calabi–Yau and Fano manifolds as well as Frobenius manifold structures on moduli…

Lyapunov exponent and topological entropy plateaus in piecewise linear maps

2013

We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.

Humbert surfaces and the Kummer plane

2003

A Humbert surface is a hypersurface of the moduli space A 2 \mathcal A_2 of principally polarized abelian surfaces defined by an equation of the form a z 1 + b z 2 + c z 3 + d ( z 2 2 − z 1 z 3 ) + e = 0 az_1+bz_2+cz_3+d(z_2^2-z_1z_3)+e=0 with integers a , … , e a,\ldots ,e . We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.

Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory

2012

We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also suggests to associate abelian varieties to polarized even weight Hodge structures. The latter construction can also be explained in terms of algebraic groups which might be useful from the point of view of Tannakian categories. The constructions depend on moduli much as in Teichm\"uller theory although the period maps in general are only real analytic. One of the nice features is how the index for certain differential operators canonically associated to …

EMERGENZA SANITARIA E TEMPORANEAITÀ

2018

Fornire risposte immediate a una modernità sempre più rivolta al rapido consumo ha dato origine a un’architettura maggiormente indirizzata alla produzione di manu- fatti provvisori e mobili. Il progetto si appropria così del tempo e ne controlla il suo stato, divenendo strumento indispensabile per rispondere a realtà in continuo divenire, spesso soggette a trasformazioni violente e repentine, come quelle generate da calamità naturali e dagli esodi conseguenti a guerre o a traumi politici, dando vi- ta a nuove forme e sistemi appartenenti a un’Architettura temporanea che potremo definire sanitaria. L’Emergenza sanitaria è una realtà ormai presente nel panorama politico, economico e sociale d…

Ras, Rap, and Rac Small GTP-binding Proteins Are Targets for Clostridium sordellii Lethal Toxin Glucosylation

1996

Lethal toxin (LT) from Clostridium sordellii is one of the high molecular mass clostridial cytotoxins. On cultured cells, it causes a rounding of cell bodies and a disruption of actin stress fibers. We demonstrate that LT is a glucosyltransferase that uses UDP-Glc as a cofactor to covalently modify 21-kDa proteins both in vitro and in vivo. LT glucosylates Ras, Rap, and Rac. In Ras, threonine at position 35 was identified as the target amino acid glucosylated by LT. Other related members of the Ras GTPase superfamily, including RhoA, Cdc42, and Rab6, were not modified by LT. Incubation of serum-starved Swiss 3T3 cells with LT prevents the epidermal growth factor-induced phosphorylation of m…