Hodge Numbers of a Kummer Covering of P2 Ramified along a Line Configuration

1988 ◽  
pp. 587-599
Author(s):  
Takayuki Oda
Author(s):  
Alice Garbagnati

Abstract We discuss the birational geometry and the Kodaira dimension of certain varieties previously constructed by Schreieder, proving that in any dimension they admit an elliptic fibration and they are not of general type. The $l$-dimensional variety $Y_{(n)}^{(l)}$, which is the quotient of the product of a certain curve $C_{(n)}$ by itself $l$ times by a group $G\simeq \left ({\mathbb{Z}}/n{\mathbb{Z}}\right )^{l-1}$ of automorphisms, was constructed by Schreieder to obtain varieties with prescribed Hodge numbers. If $n=3^c$ Schreieder constructed an explicit smooth birational model of it, and Flapan proved that the Kodaira dimension of this smooth model is 1, if $c>1$; if $l=2$ it is a modular elliptic surface; if $l=3$ it admits a fibration in K3 surfaces. In this paper we generalize these results: without any assumption on $n$ and $l$ we prove that $Y_{(n)}^{(l)}$ admits many elliptic fibrations and its Kodaira dimension is at most 1. Moreover, if $l=2$, its minimal resolution is a modular elliptic surface, obtained by a base change of order $n$ on a specific extremal rational elliptic surface; if $l\geq 3$ it has a birational model that admits a fibration in K3 surfaces and a fibration in $(l-1)$-dimensional varieties of Kodaira dimension at most 0.


2021 ◽  
Vol 378 ◽  
pp. 107436
Author(s):  
Andrew Harder
Keyword(s):  

Author(s):  
Mirko Mauri

AbstractThe moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.


2009 ◽  
Vol 39 (5) ◽  
pp. 412-417 ◽  
Author(s):  
Fortunato Morabito ◽  
Angela Tassinari ◽  
Vincenzo Callea ◽  
Maura Brugiatelli ◽  
Maria Teresa Fierro ◽  
...  

2014 ◽  
Vol 16 (02) ◽  
pp. 1350010 ◽  
Author(s):  
GILBERTO BINI ◽  
FILIPPO F. FAVALE ◽  
JORGE NEVES ◽  
ROBERTO PIGNATELLI

We classify the subgroups of the automorphism group of the product of four projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi–Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is nontrivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K2 = 3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.


Author(s):  
Vincenzo Nava ◽  
Marin Rajic ◽  
Carlos Guedes Soares

The aim of this paper is to study the dynamics of a floating body with characteristics comparable to a point absorber wave energy converter with different mooring systems, in geometrical configuration or in the materials. To this purpose, the dynamics of a moored buoy is investigated. The point absorber is modeled as a spherical buoy in plane two-dimensional motion, and it is studied under the action of irregular unidirectional wind-generated waves, moored to the seabed by means of one, two or three mooring lines. Two different sets of moorings are considered, and typical wires and chains used in offshore technology are considered, leading to a total of 6 case studies. A quasi-static approach is used for modeling the restoring forces needed to keep buoy into station, using an innovative iterative procedure able to predict for each time instant and for each cable the lay down length of the cable, being each mooring line allowed to be taut or slack. Approaches in the time and frequency domains are used to obtain the system responses in intermediate waters, where these facilities are usually installed. Results for all case studies are compared both in terms of statistics of response and tensions on the top of the cable.


Oryx ◽  
2020 ◽  
pp. 1-10 ◽  
Author(s):  
Ana Teresa Marques ◽  
Ricardo C. Martins ◽  
João Paulo Silva ◽  
Jorge M. Palmeirim ◽  
Francisco Moreira

Abstract Collision with power lines is a major cause of mortality for many bird species. Understanding the biotic and abiotic factors that increase collision risk is therefore important for implementing mitigation measures to minimize mortality, such as power line rerouting or wire marking. Here, we used collision events registered during 2003–2015 along 280 km of transmission power lines in southern Portugal to analyse spatio-temporal patterns and collision risk factors in two sympatric, threatened, and collision-prone species: the great bustard Otis tarda and the little bustard Tetrax tetrax. The occurrence of collisions was not uniform across space and time, and variations could be explained by the species' ecological requirements, distribution patterns and behaviour. Although both species fly considerable distances between areas of suitable habitat, collisions were far more likely in power line sections with > 20% (for the little bustard) or > 50% (for the great bustard) of open farmland habitat in the surroundings. Power line configuration was also important: taller pylons and those with a higher number of wire levels posed a higher risk for both species. Wire marking had a small but significant effect for the little bustard, reducing collisions risk. There was, however, no similar effect for the great bustard, possibly a result of limited data. Mitigation measures should be implemented to prevent bustard collisions, including adequate route planning, ideally avoiding areas with > 20% of open habitat. Line configuration and wire marking are particularly important where such localities cannot be avoided and power lines cross areas with a high proportion of bustard habitat, including outside protected areas.


Sign in / Sign up

Export Citation Format

Share Document