Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
We study the geometry of smooth projective surfaces defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces extremal surfaces, and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces. For instance, extremal surfaces have many lines but no triangles, hence many “star points” analogous to Eckardt points on a cubic surface. We generalize the classical notion of a double six for cubic surfaces to a double 2d on an extremal surface of degree d. We show that, asymptotically in d, smooth extremal surfaces have at least (1/16)d^{14} double 2d's. A key element of the proofs is the large automorphism group of an extremal surface, which we show to act transitively on many associated sets, such as the set of triples of skew lines on the extremal surface.more » « lessFree, publicly-accessible full text available May 15, 2025
-
Abstract Arctic amplification (AA), defined as the enhanced warming of the Arctic compared to the global average, is a robust feature of historical observations and simulations of future climate. Despite many studies investigating AA mechanisms, their relative importance remains contested. In this study, we examine the different timescales of these mechanisms to improve our understanding of AA’s fundamental causes. We use the Community Earth System Model v1, Large Ensemble configuration (CESM-LE), to generate large ensembles of 2 years simulations subjected to an instantaneous quadrupling of CO2. We show that AA emerges almost immediately (within days) following CO2increase and before any significant loss of Arctic sea ice has occurred. Through a detailed energy budget analysis of the atmospheric column, we determine the time-varying contributions of AA mechanisms over the simulation period. Additionally, we examine the dependence of these mechanisms on the season of CO2quadrupling. We find that the surface heat uptake resulting from the different latent heat flux anomalies between the Arctic and global average, driven by the CO2forcing, is the most important AA contributor on short (<1 month) timescales when CO2is increased in January, followed by the lapse rate feedback. The latent heat flux anomaly remains the dominant AA mechanism when CO2is increased in July and is joined by the surface albedo feedback, although AA takes longer to develop. Other feedbacks and energy transports become relevant on longer (>1 month) timescales. Our results confirm that AA is an inherently fast atmospheric response to radiative forcing and reveal a new AA mechanism.
-
Abstract We find a formula, in terms of , and , for the value of the ‐pure threshold for the generic homogeneous polynomial of degree in variables over an algebraically closed field of characteristic . We also show that in every characteristic and for all not divisible by , there
always exist reduced polynomials of degree in whose ‐pure threshold is a truncation of the base expansion of at some place; in particular, there always exist reduced polynomials whose ‐pure threshold isstrictly less than . We provide an example to resolve, negatively, a question proposed by Hernandez, Núñez‐Betancourt, Witt, and Zhang, as to whether a list of necessary restrictions they prove on the ‐pure threshold of reduced forms are “minimal” for . On the other hand, we also provide evidence supporting and refining their ideas, including identifying specific truncations of the base expansion of that are always ‐pure thresholds for reduced forms of degree , and computations that show their conditions suffice (inevery characteristic) for degrees up to eight and several other situations. -
We prove that if f f is a reduced homogeneous polynomial of degree d d , then its F F -pure threshold at the unique homogeneous maximal ideal is at least 1 d − 1 \frac {1}{d-1} . We show, furthermore, that its F F -pure threshold equals 1 d − 1 \frac {1}{d-1} if and only if f ∈ m [ q ] f\in \mathfrak m^{[q]} and d = q + 1 d=q+1 , where q q is a power of p p . Up to linear changes of coordinates (over a fixed algebraically closed field), we classify such “extremal singularities”, and show that there is at most one with isolated singularity. Finally, we indicate several ways in which the projective hypersurfaces defined by such forms are “extremal”, for example, in terms of the configurations of lines they can contain.more » « less
-
Abstract Historical ecology has revolutionized our understanding of fisheries and cultural landscapes, demonstrating the value of historical data for evaluating the past, present, and future of Earth’s ecosystems. Despite several important studies, Indigenous fisheries generally receive less attention from scholars and managers than the 17th–20th century capitalist commercial fisheries that decimated many keystone species, including oysters. We investigate Indigenous oyster harvest through time in North America and Australia, placing these data in the context of sea level histories and historical catch records. Indigenous oyster fisheries were pervasive across space and through time, persisting for 5000–10,000 years or more. Oysters were likely managed and sometimes “farmed,” and are woven into broader cultural, ritual, and social traditions. Effective stewardship of oyster reefs and other marine fisheries around the world must center Indigenous histories and include Indigenous community members to co-develop more inclusive, just, and successful strategies for restoration, harvest, and management.more » « less
-
Abstract This study investigates the stratospheric response to Arctic sea ice loss and subsequent near-surface impacts by analyzing 200-member coupled experiments using the Whole Atmosphere Community Climate Model version 6 (WACCM6) with preindustrial, present-day, and future sea ice conditions specified following the protocol of the Polar Amplification Model Intercomparison Project. The stratospheric polar vortex weakens significantly in response to the prescribed sea ice loss, with a larger response to greater ice loss (i.e., future minus preindustrial) than to smaller ice loss (i.e., future minus present-day). Following the weakening of the stratospheric circulation in early boreal winter, the coupled stratosphere–troposphere response to ice loss strengthens in late winter and early spring, projecting onto a negative North Atlantic Oscillation–like pattern in the lower troposphere. To investigate whether the stratospheric response to sea ice loss and subsequent surface impacts depend on the background oceanic state, ensemble members are initialized by a combination of varying phases of Atlantic multidecadal variability (AMV) and interdecadal Pacific variability (IPV). Different AMV and IPV states combined, indeed, can modulate the stratosphere–troposphere responses to sea ice loss, particularly in the North Atlantic sector. Similar experiments with another climate model show that, although strong sea ice forcing also leads to tighter stratosphere–troposphere coupling than weak sea ice forcing, the timing of the response differs from that in WACCM6. Our findings suggest that Arctic sea ice loss can affect the stratospheric circulation and subsequent tropospheric variability on seasonal time scales, but modulation by the background oceanic state and model dependence need to be taken into account.
Significance Statement This study uses new-generation climate models to better understand the impacts of Arctic sea ice loss on the surface climate in the midlatitudes, including North America, Europe, and Siberia. We focus on the stratosphere–troposphere pathway, which involves the weakening of stratospheric winds and its downward coupling into the troposphere. Our results show that Arctic sea ice loss can affect the surface climate in the midlatitudes via the stratosphere–troposphere pathway, and highlight the modulations from background mean oceanic states as well as model dependence.
-
Gillikin, David P. (Ed.)Circular shell rings along the South Atlantic Coast of North America are the remnants of some of the earliest villages that emerged during the Late Archaic (5000–3000 BP). Many of these villages, however, were abandoned during the Terminal Late Archaic (ca 3800–3000 BP). We combine Bayesian chronological modeling with mollusk shell geochemistry and oyster paleobiology to understand the nature and timing of environmental change associated with the emergence and abandonment of circular shell ring villages on Sapelo Island, Georgia. Our Bayesian models indicate that Native Americans occupied the three Sapelo shell rings at varying times with some generational overlap. By the end of the complex’s occupation, only Ring III was occupied before abandonment ca. 3845 BP. Ring III also consists of statistically smaller oysters harvested from less saline estuaries compared to earlier occupations. Integrating shell biochemical and paleobiological data with recent tree ring analyses shows a clear pattern of environmental fluctuations throughout the period in which the rings were occupied. We argue that as the environment became unstable around 4300 BP, aggregation at villages provided a way to effectively manage fisheries that are highly sensitive to environmental change. However, with the eventual collapse of oyster fisheries and subsequent rebound in environmental conditions ca. post-3800 BP, people dispersed from shell rings, and shifted to non-marine subsistence economies and other types of settlements. This study provides the most comprehensive evidence for correlations between large-scale environmental change and societal transformations on the Georgia coast during the Late Archaic period.more » « less
-
Miller, Claudia ; Striuli, Janet ; Witt, Emily E. (Ed.)Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the 19-dimensional space of all cubics, and that up to projective equivalence, there are finitely many non-Frobenius split cubic surfaces. We explicitly describe defining equations for each and characterize them as extremal in terms of configurations of lines on them. In particular, a (possibly singular) cubic surface in characteristic two fails to be Frobenius split if and only if no three lines on it form a “triangle”.more » « less