Geometric collections and Castelnuovo-Mumford Regularity

The paper begins by overviewing the basic facts on geometric exceptional collections. Then, we derive, for any coherent sheaf \cF on a smooth projective variety with a geometric collection, two spectral sequences: the first one abuts to \cF and the second one to its cohomology. The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on smooth projective varieties $X$ with a geometric collection $\sigma$. We define the notion of regularity of a coherent sheaf \cF on $X$ with respect to $\sigma$. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we show that in case of coherent sheaves on \PP^n and for a suitable geometric collection of coherent sheaves on \PP^n both notions of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a smooth quadric hypersurface Q_n \subset \PP^{n+1} ($n$ odd) with respect to a suitable geometric collection and we compare it with the Castelnuovo-Mumford regularity of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg

Getting to know you: Accuracy and error in judgments of character

Character judgments play an important role in our everyday lives. However, decades of empirical research on trait attribution suggest that the cognitive processes that generate these judgments are prone to a number of biases and cognitive distortions. This gives rise to a skeptical worry about the epistemic foundations of everyday characterological beliefs that has deeply disturbing and alienating consequences. In this paper, I argue that this skeptical worry is misplaced: under the appropriate informational conditions, our everyday character-trait judgments are in fact quite trustworthy. I then propose a mindreading-based model of the socio-cognitive processes underlying trait attribution that explains both why these judgments are initially unreliable, and how they eventually become more accurate

The determination of integral closures and geometric applications

We express explicitly the integral closures of some ring extensions; this is done for all Bring-Jerrard extensions of any degree as well as for all general extensions of degree < 6; so far such an explicit expression is known only for degree < 4 extensions. As a geometric application we present explicitly the structure sheaf of every Bring-Jerrard covering space in terms of coefficients of the equation defining the covering; in particular, we show that a degree-3 morphism f : Y --> X is quasi-etale if and only if the first Chern class of the sheaf f_*(O_Y) is trivial (details in Theorem 5.3). We also try to get a geometric Galoisness criterion for an arbitrary degree-n finite morphism; this is successfully done when n = 3 and less satifactorily done when n = 5.Comment: Advances in Mathematics, to appear (no changes, just add this info

The hidden costs of dietary restriction: Implications for its evolutionary and mechanistic origins

Dietary restriction (DR) extends life span across taxa. Despite considerable research, universal mechanisms of DR have not been identified, limiting its translational potential. Guided by the conviction that DR evolved as an adaptive, pro-longevity physiological response to food scarcity, biomedical science has interpreted DR as an activator of pro-longevity molecular pathways. Current evolutionary theory predicts that organisms invest in their soma during DR, and thus when resource availability improves, should outcompete rich-fed controls in survival and/or reproduction. Testing this prediction in Drosophila melanogaster (N > 66,000 across 11 genotypes), our experiments revealed substantial, unexpected mortality costs when flies returned to a rich diet following DR. The physiological effects of DR should therefore not be interpreted as intrinsically pro-longevity, acting via somatic maintenance. We suggest DR could alternatively be considered an escape from costs incurred under nutrient-rich conditions, in addition to costs associated with DR

On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

Unique geometry of sister kinetochores in human oocytes during meiosis I may explain maternal age-associated increases in chromosomal abnormalities

The first meiotic division in human oocytes is highly error-prone and contributes to the uniquely high incidence of aneuploidy observed in human pregnancies. A successful meiosis I (MI) division entails separation of homologous chromosome pairs and co-segregation of sister chromatids. For this to happen, sister kinetochores must form attachments to spindle kinetochore-fibres emanating from the same pole. In mouse and budding yeast, sister kinetochores remain closely associated with each other during MI, enabling them to act as a single unified structure. However, whether this arrangement also applies in human meiosis I oocytes was unclear. In this study, we perform high-resolution imaging of over 1900 kinetochores in human oocytes, to examine the geometry and architecture of the human meiotic kinetochore. We reveal that sister kinetochores in MI are not physically fused, and instead individual kinetochores within a pair are capable of forming independent attachments to spindle k-fibres. Notably, with increasing female age, the separation between kinetochores increases, suggesting a degradation of centromeric cohesion and/or changes in kinetochore architecture. Our data suggest that the differential arrangement of sister kinetochores and dual k-fibre attachments may explain the high proportion of unstable attachments that form in MI and thus indicate why human oocytes are prone to aneuploidy, particularly with increasing maternal age

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

GG-prime and GG-primary GG-ideals on GG-schemes

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$-primary decomposition and the well-definedness of $G$-associated $G$-primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$-regular and $F$-rational properties.Comment: 54pages, added Example 6.16 and the reference [8]. The final versio

Immature oocytes grow during in vitro maturation culture

BACKGROUND. Oocyte competence for maturation and embryogenesis is associated with oocyte diameter in many mammals. This study aimed to test whether such a relationship exists in humans and to quantify its impact upon in vitro maturation (IVM). METHODS. We used computer-assisted image analysis daily to measure average diameter, zona thickness and other parameters in oocytes. Immature oocytes originated from unstimulated patients with polycystic ovaries, and from stimulated patients undergoing ICSI. They were cultured with or without meiosis activating sterol (FF-MAS). Oocytes maturing in vitro were inseminated using ICSI and embryo development was monitored. A sample of freshly collected in vivo matured oocytes from ICSI patients were also measured. RESULTS. Immature oocytes were usually smaller at collection than in vivo matured oocytes. Capacity for maturation was related to oocyte diameter and many oocytes grew in culture. FF-MAS stimulated growth in ICSI derived oocytes, but only stimulated growth in PCO derived oocytes if they eventually matured in vitro. Oocytes degenerating showed cytoplasmic shrinkage. Neither zona thickness, perivitelline space, nor the total diameter of the oocyte including the zona were informative regarding oocyte maturation capacity. CONCLUSIONS. Immature oocytes continue growing during maturation culture. FF-MAS promotes oocyte growth in vitro. Oocytes from different sources have different growth profiles in vitro. Measuring diameters of oocytes used in clinical IVM may provide additional non-invasive information that could potentially identify and avoid the use of oocytes that remain in the growth phase