The embedding theorem in Hurwitz-Brill-Noether Theory

We generalize the Embedding Theorem of Eisenbud-Harris from classical Brill-Noether theory to the setting of Hurwitz-Brill-Noether theory. More precisely, in classical Brill-Noether theory, the embedding theorem states that a general linear series of degree d and rank r on a general curve of genus g is an embedding if r is at least 3. If $f \colon C \to \mathbb{P}^1$ is a general cover of degree k, and L is a line bundle on C, recent work of the authors shows that the splitting type of $f_* L$ provides the appropriate generalization of the pair (r, d) in classical Brill--Noether theory. In the context of Hurwitz-Brill-Noether theory, the condition that r is at least 3 is no longer sufficient to guarantee that a general such linear series is an embedding. We show that the additional condition needed to guarantee that a general linear series |L| is an embedding is that the splitting type of $f_* L$ has at least three nonnegative parts. This new extra condition reflects the unique geometry of k-gonal curves, which lie on scrolls in $\mathbb{P}^r$

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In Solidarity

This edition of Next Page is a departure from our usual question and answer format with a featured campus reader. Instead, we asked speakers who participated in the College’s recent Student Solidarity Rally (March 1, 2017) to recommend readings that might further our understanding of the topics on which they spoke

The Effect of Plastic Bags on Decomposition and Necrophagous Fly Composition

Forensic entomology uses insects to help estimate the post-mortem interval (PMI) based on blow fly colonization. The PMI provides an estimate of the time between death and discovery and is of extreme relevance due to its large role in forensic investigations. Nine fetal pigs were thawed from frozen 24 hours before the start of the experiment. Six fetal pigs were covered with plastic bags: three with thin plastic bags (average bag weight of 5.43 g) and three with thick plastic bags (average bag weight of 11.9 g). The remaining three pigs served as the control group. These pigs were placed outside, monitored for 6 days, and checked three times daily to look for the presence of blow fly eggs, adults, and maggots. Third instar maggots were collected for later observance. ANOVA tests were conducted to look for differences in the timing of blow fly oviposition between treatments. There was no significant difference found for any of the life stages in either trial. P-values ranged from 0.22 -1. The maggots were identified to species to look for differences in species composition between treatments. Lucilia coeruleiviridis was the dominant species found. Sarcophagidae flies were found only on bagged pigs. Sarcophagidae larvae have been found very rarely in this field site over the past decade, so this is an interesting finding. Scavenging of the pigs was a problem and future research should aim to reduce the effects of vertebrate scavenging

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Idiopathic Hemochromotosis and Alpha‐1‐Antitrypsin Deficiency: Coexistence in a Family with Progressive Liver Disease in the Proband

A patient with coexistent hemochromatosis and alpha‐1‐antitrypsin deficiency which led to cirrhosis and death despite adequate therapy for hemochromatosis is reported. Evaluation of the family revealed first degree relatives with iron overload and others with alpha‐1‐antitrypsin deficiency but none with both conditions. The role of family studies in the early recognition and possible prevention of overt clinical disease in individuals with either of these two genetic diseases is discussed. Copyright © 1983 American Association for the Study of Liver Disease