An inclusion result for dagger closure in certain section rings of abelian varieties

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.Comment: 11 pages, v2: updated one reference, fixed 2 typos; final versio

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

Generalised Moore spectra in a triangulated category

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which "approximates" objects of the module category of the endomorphism algebra of C in T. This generalises and extends a construction of Jorgensen in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding the module category in a triangulated category. As an example of the theory, we recover Keller's canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category for u>1.Comment: 26 pages, improvement to exposition of the proof of Theorem 3.

A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra

A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to show the abundance of elements of N_p. Our main result shows that any divisor n of q-1, where q is a power of p, such that $n\ge (p-1)^{1/p} (q-1)^{1-1/(2p)}$, belongs to N_p. This extends its special case for p=2 which was proved in a previous paper by a different method.Comment: 10 pages. This version has been revised according to a referee's suggestions. The additions include a discussion of the (lower) density of the set N_p, and the results of more extensive machine computations. Note that the title has also changed. To appear in Israel J. Mat

3 Published Papers

(I) The System Ferrous Oxide-Phosphoric Acid-Water and some of its Oxidation Products. The existence of the monohydrogen ferrous phosphate Fe(HPO4),H20 (or 2FeO, P2O5, 3H 2O) has "been confirmed. This com-pound was described by Debray but subsequently Erlenmeyer cast doubt on Debray's results. The compound has been obtained in two forms, viz. "amorphous" and crystalline, the latter showing a decidedly lower solubility. In addition a dihydrate Fe(HPO4), 2H2O (or 2FeO, P2O5, 5H2O) has been shown to exist. The dihydrogen phosphate Fe(H2PO4) 2, 2H2O (or FeO, P2O5, 4H2O) described by Erlenmeyer has been confirmed. It is thought that the ferrous phosphates are not complex. By the oxidatiod of phase mixtures poor in acid a red-brown ferric phosphate betaFe 2O3, P2O5, 4H2O is deposited, which is only stable when ferrous iron is present in the liquid phase (at 70&deg;). By completing the oxidation the substance changes both in crystalline form and colour (to pink) to a solid having the same empirical composition. It is thought2that the latter is a complex ferri-phosphate, whilst the former is a true ferric phosphate. (II) An Aeparatus for the Viscosimetric Determination of Transition Points. By means of an apparatus combining the functions of a viscometer and a stirrer the transition points Na2SO4, 10 &harr; OH2O, NiSO4, 7 &harr; 6H2O, and Na2HPO4, 12 &harr; 7H2O have been determined. (III) The System Ferric Oxide-Arsenic Acid-Water at Low Concentrations of Arsenic Acid. The following solid phases have been found to exist between 2&middot;6 and 23&middot;13% of As2O5 in the liquid phase at 25&deg;: Fe2O3, As2O 5, xH2O (where x is probably near 6); Fe 2O3, 2As2O5, 8H2O. The latter compound has not been described before as far as is known. Its existence provides evidence that the ferric arsenates, like the phosphates, are complex. No basic salts were obtained. The system was characterised by an extreme sluggishness in approaching equilibrium.<p

On the ideals of equivariant tree models

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.Comment: 23 pages. Greatly improved exposition, in part following suggestions by a referee--thanks! Also added exampl

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

Non-linear Yang-Mills instantons from strings are π\pi-stable D-branes

We show that B-type $\Pi$-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang--Mills equations for the non-linear deformations of Yang--Mills instantons that appear in the low-energy geometric limit of strings exist iff they are $\pi$-stable, a geometric large volume version of $\Pi$-stability. This shows that $\pi$-stability is the correct physical stability concept. We speculate that this string-canonical choice of stable objects, which is encoded in and derived from the central charge of the string-\emph{algebra}, should find applications to algebraic geometry where there is no canonical choice of stable \emph{geometrical} objects.Comment: v3: Minor revision; 14 page

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