Counting curves over finite fields

This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of cardinality q, but the main emphasis is on results on the Euler characteristic of the cohomology of local systems on moduli spaces of curves of low genus and its implications for modular forms.Comment: 25 pages, to appear in Finite Fields and their Application

Cohomology of local systems on loci of d-elliptic abelian surfaces

We consider the loci of d-elliptic curves in $M_2$, and corresponding loci of d-elliptic surfaces in $A_2$. We show how a description of these loci as quotients of a product of modular curves can be used to calculate cohomology of natural local systems on them, both as mixed Hodge structures and $\ell$-adic Galois representations. We study in particular the case d=2, and compute the Euler characteristic of the moduli space of n-pointed bi-elliptic genus 2 curves in the Grothendieck group of Hodge structures.Comment: 15 pages, complete re-write of earlier versio

Tautological classes on the moduli space of hyperelliptic curves with rational tails

We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. (C) 2017 Elsevier B.V. All rights reserved11sci

Leptospira infection among pigs in southern Vietnam

Leptospirosis is a bacterial disease that in pigs primarily causes reproductive disturbances. The disease is a zoonosis, i.e. it can be transmitted between animals and humans. Leptospirosis is spread worldwide, although it is of most importance in tropical regions where animal management and climate favour transmission and survival of the bacteria in the environment, such as the tropical Mekong delta (MD) in southern Vietnam. In the MD, reproduction disturbances in pigs due to infectious agents are of concern. This thesis investigates Leptospira infection among pigs in the MD with aspects on epidemiology, clinical affection and bacteriology. Such information is of importance if preventive measures are to be implemented. This study showed that leptospiral seroprevalences among sows were high and that a larger proportion of sows on small-scale farms compared with large-scale farms were seropositive. Few risk factors were found that could explain seropositivity in the sows. It was also found that the seroprevalences for some serovars were higher during the dry period compared with the wet period. Furthermore, some serovars were associated with impaired reproductive performance of the sows, such as an increased number of piglets born dead per litter and a longer weaning to service interval. Also, seroprevalences among fattening pigs at slaughter were high, and in these animals leptospires were demonstrated in a large number of kidneys with macro- and microscopic kidney lesions. One leptospiral serovar was isolated from a kidney. Taken together, Leptospira infection, indicated by seropositivity, is common among pigs in the MD, which may be explained by a favourable environment rather than certain risk factors. Small-scale farms are in closer contact with the surrounding environment than large-scale farms, which may explain the differences between the farming systems. Even in regions with high leptospiral seroprevalences, infection, as indicated by seropositivity, has a negative impact on the reproductive performance of sows. Furthermore, a large proportion of fatteners with macroscopic renal lesions carry the bacteria, which constitutes a health hazard for personnel at abattoirs and persons exposed elsewhere