Could H.P. Lovecraft Create a Semblance of Normality?

As part of historically minorized culture, Catalan literature endured difficult periods, e.g., the Francoist regime. To imagine different worlds writing in this language was even more arduous in the 20th century because of the negative attitude towards the fantastic shared by two fundamental trends of Catalan literature up to the 1970s: Noucentisme and historical realism. Nonetheless, H.P. Lovecraft was an important reference in the Catalan non-mimetic fiction that had a certain revival in post-war times. As a step towards “normalization” of Catalan literature after Franco’s death, the writers’ collective Ofèlia Dracs published several collections of short-stories of “genre” fiction–among them Lovecraft, Lovecraft! (1981). On the one hand, this article inscribes this exceptional collection in its historical context and in the contemporary Catalan literary system; on the other, it aims to shed light on Lovecraft’s role in Ofèlia Dracs’ book, proving the projection of his extraordinary supernatural world onto it by the presence not only of Lovecraftian hypotexts in its different tales, but also of metafictional elements inherited mainly from Joan Perucho’s postmodernist writings.

Residual categories for (co)adjoint Grassmannians in classical types

In our previous paper we suggested a conjecture relating the structure of the small quantum cohomology ring of a smooth Fano variety of Picard number 1 to the structure of its derived category of coherent sheaves. Here we generalize this conjecture, make it more precise, and support it by the examples of (co)adjoint homogeneous varieties of simple algebraic groups of Dynkin types $\mathrm {A}_n$ and $\mathrm {D}_n$ , that is, flag varieties $\operatorname {Fl}(1,n;n+1)$ and isotropic orthogonal Grassmannians $\operatorname {OG}(2,2n)$ ; in particular, we construct on each of those an exceptional collection invariant with respect to the entire automorphism group. For $\operatorname {OG}(2,2n)$ this is the first exceptional collection proved to be full.

Stringy Kähler Moduli for the Pfaffian-Grassmannian Correspondence

The Pfaffian-Grassmannian correspondence relates certain pairs of derived equivalent non-birational Calabi-Yau 3-folds. Given such a pair, I construct a set of derived equivalences corresponding to mutations of an exceptional collection on the relevant Grassmannian, and give a mirror symmetry interpretation, following a physical analysis of Eager, Hori, Knapp, and Romo.

Exceptional collections on certain Hassett spaces

We construct an $S_2\times S_n$ invariant full exceptional collection on Hassett spaces of weighted stable rational curves with $n+2$ markings and weights $(\frac{1}{2}+\eta, \frac{1}{2}+\eta,\epsilon,\ldots,\epsilon)$, for $0<\epsilon, \eta\ll1$ and can be identified with symmetric GIT quotients of $(\mathbb{P}^1)^n$ by the diagonal action of $\mathbb{G}_m$ when $n$ is odd, and their Kirwan desingularization when $n$ is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full $S_n$-invariant exceptional collection on $\overline{\mathcal{M}}_{0,n}$. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev-Manin spaces. Comment: At the request of the referee, the paper arXiv:1708.06340 has been split into two parts. This is the second of those papers (submitted). 36 pages

In-place molecular preservation of cellulose in 5,000-year-old archaeological textiles

The understanding of fossilization mechanisms at the nanoscale remains extremely challenging despite its fundamental interest and its implications for paleontology, archaeology, geoscience, and environmental and material sciences. The mineralization mechanism by which cellulosic, keratinous, and silk tissues fossilize in the vicinity of archaeological metal artifacts offers the most exquisite preservation through a mechanism unexplored on the nanoscale. It is at the center of the vast majority of ancient textiles preserved under nonextreme conditions, known through extremely valuable fragments. Here we show the reconstruction of the nanoscale mechanism leading to the preservation of an exceptional collection of ancient cellulosic textiles recovered in the ancient Near East (4,000 to 5,000 years ago). We demonstrate that even the most mineralized fibers, which contain inorganic compounds throughout their histology, enclose preserved cellulosic remains in place. We evidence a process that combines the three steps of water transport of biocidal metal cations and soil solutes, degradation and loss of crystallinity of cellulosic polysaccharides, and silicification.

The small quantum cohomology of the Cayley Grassmannian

We compute the small cohomology ring of the Cayley Grassmannian, that parametrizes four-dimensional subalgebras of the complexified octonions. We show that all the Gromov–Witten invariants in the multiplication table of the Schubert classes are nonnegative and deduce Golyshev’s conjecture [Formula: see text] holds true for this variety. We also check that the quantum cohomology is semisimple and that there exists, as predicted by Dubrovin’s conjecture, an exceptional collection of maximal length in the derived category.

Kaunas of 1919-1939: a temporary capital built by its citizens

W latach 1919-1939, wskutek sytuacji politycznej, Kowno zyskało status tymczasowej stolicy Litwy. Te dwie dekady, w czasie których miasto było centrum wielu ważkich wydarzeń politycznych, ekonomicznych i kulturalnych, znacznie przyczyniły się do stworzenia tożsamości Kowna. W tym okresie miał miejsce boom architektoniczny, który zaowocował pojawieniem się wyjątkowej grupy budynków, charakteryzujących się unikalnym połączeniem rozmaitych wpływów i interpretacji modernizmu oraz narodowego romantyzmu. Niniejszy artykuł przedstawia historyczny przegląd kulturalnych i ekonomicznych okoliczności, które wpłynęły na rozwój budownictwa w Kownie w okresie dwudziestolecia międzywojennego. Due to the political circumstances from 1919 to 1939 the city of Kaunas had a status of provisional capital of Lithuania. Two decades of being at the epicentre of political, economic and cultural events greatly contributed to the creation of the city‘s identity. Construction boom of these years left an exceptional collection of architecture behind, with a unique combination of different influences and interpretations of modernism and national romanticism. This article will give a historical overview of cultural and economic circumstances which influenced architectural development between two World Wars.

TILTING THEORY FOR GORENSTEIN RINGS IN DIMENSION ONE

In representation theory, commutative algebra and algebraic geometry, it is an important problem to understand when the triangulated category $\mathsf{D}_{\operatorname{sg}}^{\mathbb{Z}}(R)=\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R$ admits a tilting (respectively, silting) object for a $\mathbb{Z}$ -graded commutative Gorenstein ring $R=\bigoplus _{i\geqslant 0}R_{i}$ . Here $\mathsf{D}_{\operatorname{sg}}^{\mathbb{Z}}(R)$ is the singularity category, and $\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R$ is the stable category of $\mathbb{Z}$ -graded Cohen–Macaulay (CM) $R$ -modules, which are locally free at all nonmaximal prime ideals of $R$ . In this paper, we give a complete answer to this problem in the case where $\dim R=1$ and $R_{0}$ is a field. We prove that $\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R$ always admits a silting object, and that $\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R$ admits a tilting object if and only if either $R$ is regular or the $a$ -invariant of $R$ is nonnegative. Our silting/tilting object will be given explicitly. We also show that if $R$ is reduced and nonregular, then its $a$ -invariant is nonnegative and the above tilting object gives a full strong exceptional collection in $\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R=\text{}\underline{\mathsf{CM}}^{\mathbb{Z}}R$ .

A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles

We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category that does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.

Luminița Duțică – An Exceptional Collection of Musical Studies

The prestigious publishing house Artes, from the capital of Moldova, offered the general public a work which encompasses studies written by the Luminița Duțică starting from her student years, going through all the professional and teaching stages of her musical career as a teacher at secondary and tertiary level, until she became Professor at “George Enescu” National University of Arts Iași. The volume contains exceptional research, benefiting from many musical well-chosen examples accompanied by detailed analysis, but also a rich reference list which entails the investigation in detail of many areas of the sonorous art. The clear and comprehensive writing is very well-suited to the pedagogical dimension of the volume, is reflected in all of the specialized writings published by an author with a vocation for teaching.