Fatighenti and Mongardi have defined Fano varieties of type S6 as zero loci of a certain vector bundle on the Grassmannian $\hbox{Gr}(2,10)$. These varieties have 3 Hodge structures of K3 type in their cohomology. We show that the Chow ring of these...
No description (⭐ 0)
A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, espec...
A $n$-dimensional Gorenstein toric Fano variety $X$ is called Del Pezzo variety if the anticanonical class $-K_X$ is a $(n-1)$-multiple of a Cartier divisor. Our purpose is to give a complete biregular classfication of Gorenstein toric Del Pezzo va...
Concerning Violence is a 2014 documentary film written and directed by Göran Hugo Olsson. It is based on Frantz Fanon's essay, "Concerning Violence", from
We give lower bounds for Hodge numbers of smooth well formed Fano weighted complete intersections. In particular, we compute their Hodge level, that is, the maximal distance between non-trivial Hodge numbers in the same row of the Hodge diamond. This...
We describe the geometry of Küchle varieties (i.e. Fano 4-folds of index 1 contained in the Grassmannians as zero loci of equivariant vector bundles) with Picard number greater than 1 and the structure of their derived categories....
...
...
Then to CNN". The New York Times. ISSN 0362-4331. Retrieved January 30, 2022. Fields, Gary (January 4, 2023). "Groups urge GOP House leaders to condemn
We give a criterion for the existence of a Kähler-Einstein metric on a Fano manifold $M$ in terms of the higher algebraic alpha-invariants $α_{m,k}(M)$....
We study the geography and birational geometry of 3-fold conic bundles over P^2 and cubic del Pezzo fibrations over P^1. We discuss many explicit examples and raise several open questions. This paper was submitted to the proceedings of the "Fano co...
An O'Nan configuration in a unital is a set of four lines forming a quadrilateral, where the six intersections of pairs of lines are points of the unital. In 2019 Feng and Li elegantly construct O'Nan configurations in orthogonal and Tits Buekenhout-...
Strong spatial confinement and highly reduced dielectric screening provide monolayer transition metal dichalcogenides (TMDCs) with strong many-body effects, thereby possessing optically forbidden excitonic states (i.e., dark excitons) at room tempera...
We investigate the behavior of light pulse propagation in a 4-level double Lambda atomic system under condition of electromagnetically induced transparency. The Fano type interference effect and spectral hole burning appears in the the dynamics of th...
Valley degree of freedom besides spin is a promising candidate as a carrier of information. Spintronics has come a long way and spin modulation can be realized by quantum interference and spin-orbit coupling effect. However, the control of valley deg...
We give the multiplicity of terminal singularities on threefolds by simple calculation. Then we obtain the best inequalities for the multiplicity and the index. By using this, we can improve the boundedness number of terminal weak Q-Fano 3-folds in...
There have been major developments in the theory of moduli of varieties in the past decade, essentially settling the construction of moduli spaces of log canonically polarized slc pairs and moduli spaces of K-polystable log Fano pairs. Given the cons...
This survey article is an accompaniment to the 2025 Summer Research Institute in Algebraic Geometry Bootcamp on K-stability and K-moduli. It is aimed at graduate students and intended to provide the necessary background to begin research on explicit...
We examine generation dynamics of coherent phonons (CPs) in both of polar and non-polar semiconductors -- such as GaAs and Si -- based on a polaronic-quasiparticle (PQ) model. In the model concerned, the PQ operator is composed of two kinds of operat...