scholarly journals Smooth Fano Intrinsic Grassmannians of Type 2,n with Picard Number Two

2021 ◽  
Author(s):  
Muhammad Imran Qureshi ◽  
Milena Wrobel
Keyword(s):  
Explicit Formula ◽  
Projective Variety ◽  
Complete Classification ◽  
Picard Number ◽  
Cox Ring

Abstract We introduce the notion of intrinsic Grassmannians that generalizes the well-known weighted Grassmannians. An intrinsic Grassmannian is a normal projective variety whose Cox ring is defined by the Plucker ideal $I_{d,n}$ of the Grassmannian $\textrm{Gr}(d,n)$. We give a complete classification of all smooth Fano intrinsic Grassmannians of type $(2,n)$ with Picard number two and prove an explicit formula to compute the total number of such varieties for an arbitrary $n$. We study their geometry and show that they satisfy Fujita’s freeness conjecture.

scholarly journals Quotients of del Pezzo surfaces

2019 ◽  
Vol 30 (12) ◽  
pp. 1950068
Author(s):  
Andrey Trepalin
Keyword(s):  
Complete Classification ◽  
Finite Subgroup ◽  
Del Pezzo Surfaces ◽  
Picard Number ◽  
Del Pezzo Surface ◽  
Cyclic Groups ◽  
Trivial Group ◽  
Quotient Surface ◽  
Del Pezzo

Let [Formula: see text] be any field of characteristic zero, [Formula: see text] be a del Pezzo surface and [Formula: see text] be a finite subgroup in [Formula: see text]. In this paper, we study when the quotient surface [Formula: see text] can be non-rational over [Formula: see text]. Obviously, if there are no smooth [Formula: see text]-points on [Formula: see text] then it is not [Formula: see text]-rational. Therefore, under assumption that the set of smooth [Formula: see text]-points on [Formula: see text] is not empty we show that there are few possibilities for non-[Formula: see text]-rational quotients. The quotients of del Pezzo surfaces of degree [Formula: see text] and greater are considered in the author’s previous papers. In this paper, we study the quotients of del Pezzo surfaces of degree [Formula: see text]. We show that they can be non-[Formula: see text]-rational only for the trivial group or cyclic groups of order [Formula: see text], [Formula: see text] and [Formula: see text]. For the trivial group and the group of order [Formula: see text], we show that both [Formula: see text] and [Formula: see text] are not [Formula: see text]-rational if the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. For the groups of order [Formula: see text] and [Formula: see text], we construct examples of both [Formula: see text]-rational and non-[Formula: see text]-rational quotients of both [Formula: see text]-rational and non-[Formula: see text]-rational del Pezzo surfaces of degree [Formula: see text] such that the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. As a result of complete classification of non-[Formula: see text]-rational quotients of del Pezzo surfaces we classify surfaces that are birationally equivalent to quotients of [Formula: see text]-rational surfaces, and obtain some corollaries concerning fields of invariants of [Formula: see text].

scholarly journals Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

2020 ◽  
Vol 31 (09) ◽  
pp. 2050066
Author(s):  
Jie Liu
Keyword(s):  
Homogeneous Space ◽  
Complete Classification ◽  
Picard Number ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Conormal Bundle ◽  
Rational Homogeneous Space

Let [Formula: see text] be an [Formula: see text]-dimensional complex Fano manifold [Formula: see text]. Assume that [Formula: see text] contains a divisor [Formula: see text], which is isomorphic to a rational homogeneous space with Picard number one, such that the conormal bundle [Formula: see text] is ample over [Formula: see text]. Building on the works of Tsukioka, Watanabe and Casagrande–Druel, we give a complete classification of such pairs [Formula: see text].

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

The challenges of diagnosing diabetes in childhood

Diagnosis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mairi Pucci ◽  
Marco Benati ◽  
Claudia Lo Cascio ◽  
Martina Montagnana ◽  
Giuseppe Lippi
Keyword(s):  
Diabetes Mellitus ◽  
Children And Young People ◽  
Narrative Literature ◽  
Diagnosis And Classification ◽  
Narrative Literature Review ◽  
Optimal Approach ◽  
Diagnostic Step

AbstractDiabetes is one of the most prevalent diseases worldwide, whereby type 1 diabetes mellitus (T1DM) alone involves nearly 15 million patients. Although T1DM and type 2 diabetes mellitus (T2DM) are the most common types, there are other forms of diabetes which may remain often under-diagnosed, or that can be misdiagnosed as being T1DM or T2DM. After an initial diagnostic step, the differential diagnosis among T1DM, T2DM, Maturity-Onset Diabetes of the Young (MODY) and others forms has important implication for both therapeutic and behavioral decisions. Although the criteria used for diagnosing diabetes mellitus are well defined by the guidelines of the American Diabetes Association (ADA), no clear indications are provided on the optimal approach to be followed for classifying diabetes, especially in children. In this circumstance, both routine and genetic blood test may play a pivotal role. Therefore, the purpose of this article is to provide, through a narrative literature review, some elements that may aid accurate diagnosis and classification of diabetes in children and young people.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Visual learning and classification of human epithelial type 2 cell images through spontaneous activity patterns

2014 ◽  
Vol 47 (7) ◽  
pp. 2325-2337 ◽  
Author(s):  
Yan Yang ◽  
Arnold Wiliem ◽  
Azadeh Alavi ◽  
Brian C. Lovell ◽  
Peter Hobson
Keyword(s):  
Spontaneous Activity ◽  
Activity Patterns ◽  
Visual Learning

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

Sign in / Sign up

Export Citation Format

Share Document