Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHodge Numbers for CICYs with Symmetries of Order Divisible by 4
157
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kahler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, $G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2 times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously. This paper deals with the remaining cases, for which $G supseteq Z_4$ or $Gsupseteq Z_2 times Z_2$. We also compute the Hodge numbers for 99 of the 166 CICYs which have $Z_2$ quotients.
rate research
Read More
We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})le 24$. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi-Yau threefolds, most of which were computed in Refs. [1-3] and the remainder in Ref. [4], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. [1, 5]. In view of this and other recent constructions of Calabi-Yau threefolds with small height, we have produced an updated list.
A p-divisible group, or more generally an F-crystal, is said to be Hodge-Newton reducible if its Hodge polygon passes through a break point of its Newton polygon. Katz proved that Hodge-Newton reducible F-crystals admit a canonical filtration called the Hodge-Newton filtration. The notion of Hodge-Newton reducibility plays an important role in the deformation theory of p-divisible groups; the key property is that the Hodge-Newton filtration of a p-divisible group over a field of characteristic p can be uniquely lifted to a filtration of its deformation. We generalize Katzs result to F-crystals that arise from an unramified local Shimura datum of Hodge type. As an application, we give a generalization of Serre-Tate deformation theory for local Shimura data of Hodge type. We also apply our deformation theory to study some congruence relations on Shimura varieties of Hodge type.
It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients -- and in particular Love numbers -- vanish. Moreover, property (1) alone is sufficient to forbid the existence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.
Let k be a perfect field of characteristic p>0. We prove the existence of ascending and descending slope filtrations for Shimura p-divisible objects over k. We use them to classify rationally these objects over bar k. Among geometric applications, we mention two. First we formulate Manin problems for Shimura varieties of Hodge type. We solve them if either pGe 3 or p=2 and two mild conditions hold. Second we formulate integral Manin problems. We solve them for certain Shimura varieties of PEL type.
We construct firstly the complete list of five quantum deformations of $D=4$ complex homogeneous orthogonal Lie algebra $mathfrak{o}(4;mathbb{C})cong mathfrak{o}(3;mathbb{C})oplus mathfrak{o}(3;mathbb{C})$, describing quantum rotational symmetry of four-dimensional complex space-time, in particular we provide the corresponding universal quantum $R$-matrices. Further applying four possible reality conditions we obtain all sixteen Hopf-algebraic quantum deformations for the real forms of $mathfrak{o}(4;mathbb{C})$: Euclidean $mathfrak{o}(4)$, Lorentz $mathfrak{o}(3,1)$, Kleinian $mathfrak{o}(2,2)$ and quaternionic $mathfrak{o}^{star}(4)$. For $mathfrak{o}(3,1)$ we only recall well-known results obtained previously by the authors, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) as well as for the complex Lie algebra $mathfrak{o}(4;mathbb{C})$ we present new results.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
