Abelian varietyIn mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.
Algebraic varietyAlgebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.
Cultural heritageCultural heritage is the heritage of tangible and intangible heritage assets of a group or society that is inherited from past generations. Not all heritages of past generations are "heritage"; rather, heritage is a product of selection by society. Cultural heritage includes tangible culture (such as buildings, monuments, landscapes, archive materials, books, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage (including culturally significant landscapes, and biodiversity).
Projective varietyIn algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .
Cultural heritage managementCultural heritage management (CHM) is the vocation and practice of managing cultural heritage. It is a branch of cultural resources management (CRM), although it also draws on the practices of cultural conservation, restoration, museology, archaeology, history and architecture. While the term cultural heritage is generally used in Europe, in the US the term cultural resources is in more general use specifically referring to cultural heritage resources.
Chow varietyIn mathematics, particularly in the field of algebraic geometry, a Chow variety is an algebraic variety whose points correspond to effective algebraic cycles of fixed dimension and degree on a given projective space. More precisely, the Chow variety is the fine moduli variety parametrizing all effective algebraic cycles of dimension and degree in . The Chow variety may be constructed via a Chow embedding into a sufficiently large projective space.
Cultural resource managementIn the broadest sense, cultural resource management (CRM) is the vocation and practice of managing heritage assets, and other cultural resources such as contemporary art. It incorporates Cultural Heritage Management which is concerned with traditional and historic culture. It also delves into the material culture of archaeology. Cultural resource management encompasses current culture, including progressive and innovative culture, such as urban culture, rather than simply preserving and presenting traditional forms of culture.
Generalized flag varietyIn mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties. Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F.
Named-entity recognitionNamed-entity recognition (NER) (also known as (named) entity identification, entity chunking, and entity extraction) is a subtask of information extraction that seeks to locate and classify named entities mentioned in unstructured text into pre-defined categories such as person names, organizations, locations, medical codes, time expressions, quantities, monetary values, percentages, etc. Most research on NER/NEE systems has been structured as taking an unannotated block of text, such as this one: Jim bought 300 shares of Acme Corp.
Conservation and restoration of cultural propertyThe conservation and restoration of cultural property focuses on protection and care of cultural property (tangible cultural heritage), including artworks, architecture, archaeology, and museum collections. Conservation activities include preventive conservation, examination, documentation, research, treatment, and education. This field is closely allied with conservation science, curators and registrars.
