scholarly journals SCHEMATIC HARDER–NARASIMHAN STRATIFICATION

2011 ◽  
Vol 22 (10) ◽  
pp. 1365-1373 ◽  
Author(s):  
NITIN NITSURE
Keyword(s):  
Base Change ◽  
Closed Subscheme ◽  
Universal Property ◽  
Coherent Sheaves ◽  
Algebraic Stack ◽  
Change Factors ◽  
The Family ◽  
Type Form ◽  
Flat Family ◽  
Parameter Scheme

For any flat family of pure-dimensional coherent sheaves on a family of projective schemes, the Harder–Narasimhan type (in the sense of Gieseker semistability) of its restriction to each fiber is known to vary semicontinuously on the parameter scheme of the family. This defines a stratification of the parameter scheme by locally closed subsets, known as the Harder–Narasimhan stratification. In this paper, we show how to endow each Harder–Narasimhan stratum with the structure of a locally closed subscheme of the parameter scheme, which enjoys the universal property that under any base change the pullback family admits a relative Harder–Narasimhan filtration with a given Harder–Narasimhan type if and only if the base change factors through the schematic stratum corresponding to that Harder–Narasimhan type. The above schematic stratification induces a stacky stratification on the algebraic stack of pure-dimensional coherent sheaves. We deduce that coherent sheaves of a fixed Harder–Narasimhan type form an algebraic stack in the sense of Artin.

scholarly journals Dinamika Kemandirian Mahasiswa Perantauan

2021 ◽  
Vol 1 (3) ◽  
pp. 167
Author(s):  
Nadia Fauzia ◽  
Asmaran Asmaran ◽  
Shanty Komalasari
Keyword(s):  
Parenting Style ◽  
Sampling Technique ◽  
Research Approach ◽  
Overseas Students ◽  
Descriptive Research ◽  
Change Factors ◽  
The Family ◽  
Qualitative Descriptive ◽  
The Subject ◽  
Selection Of

The purpose of this study is to discuss the dynamics of the independence of UIN Antasari Banjarmasin students and what factors are behind the independence of UIN Antasari Banjarmasin students. The reason is because overseas there are changes in conditions and situations, so that students who leave will experience dynamics of independence. This type of research is a qualitative descriptive research approach. Selection of subjects using purposive sampling technique, which is based on the characteristics of the subject in accordance with the research objectives to be carried out. The object of this research is the dynamics of independence, the subject is 5 overseas students. Data collection techniques using interviews and observations. Based on the results of research that overseas students of UIN Antasari Banjarmasin need a process to be independent in living their lives overseas. That is because overseas there has been a change. Factors that influence the dynamics of independence of overseas students at UIN Antasari Banjarmasin are factors of parenting style, the order of children in the family, age and the education system in schools.

scholarly journals Base change for semiorthogonal decompositions

2011 ◽  
Vol 147 (3) ◽  
pp. 852-876 ◽  
Author(s):  
Alexander Kuznetsov
Keyword(s):  
Algebraic Variety ◽  
Base Change ◽  
Derived Category ◽  
Intermediate Step ◽  
Coherent Sheaves ◽  
Base Scheme ◽  
Compatible System ◽  
Perfect Complexes

AbstractLet X be an algebraic variety over a base scheme S and ϕ:T→S a base change. Given an admissible subcategory 𝒜 in 𝒟b(X), the bounded derived category of coherent sheaves on X, we construct under some technical conditions an admissible subcategory 𝒜T in 𝒟b(X×ST), called the base change of 𝒜, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of 𝒟b (X) is given, then the base changes of its components form a semiorthogonal decomposition of 𝒟b (X×ST) . As an intermediate step, we construct a compatible system of semiorthogonal decompositions of the unbounded derived category of quasicoherent sheaves on X and of the category of perfect complexes on X. As an application, we prove that the projection functors of a semiorthogonal decomposition are kernel functors.

Geometry of projection-generic space curves

2009 ◽  
Vol 147 (1) ◽  
pp. 115-142
Author(s):  
C. T. C. WALL
Keyword(s):  
Local Structure ◽  
Double Point ◽  
Normal Forms ◽  
Blow Up ◽  
Complex Case ◽  
Plane Curves ◽  
Space Curves ◽  
Open Set ◽  
The Family ◽  
Flat Family

AbstractIn earlier work I defined a class of curves, forming a dense open set in the space of maps from S1 to P3, such that the family of projections of a curve in this class is stable under perturbations of C: we call the curves in the class projection-generic. The definition makes sense also in the complex case. The partition of projective space according to the singularities of the corresponding projection of C is a stratification. Its local structure outside C is the same as that of the versal unfoldings of the singularities presented.To study points on C we introduce the blow-up BC of P3 along C, and a family of plane curves, parametrised by z ∈ BC; we saw in the earlier work that this is a flat family.Here we show that near most z ∈ BC, the family gives a family of parametrised germs which versally unfolds the singularities occurring. Otherwise we find that the double point number δ of Γz drops by 1 for z ∉ EC. We establish a theory of versality for unfoldings of A or D singularities such that δ drops by at most 1, and show that in the remaining cases, we have an unfolding which is versal in this sense.This implies normal forms for the stratification of BC; further work allows us to derive local normal forms for strata of the stratification of P3.

scholarly journals Duality for Commutative Group Stacks

2019 ◽  
Author(s):  
Sylvain Brochard
Keyword(s):  
Sufficient Conditions ◽  
Number Fields ◽  
Commutative Group ◽  
The Other ◽  
Universal Property ◽  
Geometric Description ◽  
Algebraic Stack ◽  
Rational Varieties ◽  
The One ◽  
Picard Functor

Abstract We study in this article the dual of a (strictly) commutative group stack $G$ and give some applications. Using the Picard functor and the Picard stack of $G$, we first give some sufficient conditions for $G$ to be dualizable. Then, for an algebraic stack $X$ with suitable assumptions, we define an Albanese morphism $a_X: X\longrightarrow A^1(X)$ where $A^1(X)$ is a torsor under the dual commutative group stack $A^0(X)$ of $\textrm{Pic}_{X/S}$. We prove that $a_X$ satisfies a natural universal property. We give two applications of our Albanese morphism. On the one hand, we give a geometric description of the elementary obstruction and of universal torsors (standard tools in the study of rational varieties over number fields). On the other hand, we give some examples of algebraic stacks that satisfy Grothendieck’s section conjecture.

Policies and Practices of Parental Notification for Student Alcohol Violations

NASPA Journal ◽  
2005 ◽  
Vol 42 (4) ◽  
Author(s):  
John W Lowery ◽  
Carolyn J. Palmer ◽  
Donald D Gehring
Keyword(s):  
Higher Education ◽  
Institutions Of Higher Education ◽  
Institutional Policies ◽  
Parental Notification ◽  
Change Factors ◽  
Educational Rights ◽  
Privacy Act ◽  
The Family ◽  
Perceived Impact ◽  
Alcohol And Other Drugs

With the passage of Higher Education Amendments of 1998, the Family Educational Rights and Privacy Act of 1974 was amended to make it substantially easier for institutions of higher education to notify parents when their students violate institutional policies or laws concerning alcohol and other drugs. This study examines how common parental notification policies are in the wake of this legislative change, factors deemed important in adopting such policies, the structure of the policies, reactions to the policies, and the perceived impact of the policies on alcohol violations.

scholarly journals Perfect complexes on algebraic stacks

2017 ◽  
Vol 153 (11) ◽  
pp. 2318-2367 ◽  
Author(s):  
Jack Hall ◽  
David Rydh
Keyword(s):  
Derived Categories ◽  
Triangulated Categories ◽  
Azumaya Algebras ◽  
Algebraic Stacks ◽  
Coherent Sheaves ◽  
Algebraic Stack ◽  
Perfect Complexes ◽  
Compactly Generated

We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

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