*Max Saunders*

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199579761
- eISBN:
- 9780191722882
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579761.003.0014
- Subject:
- Literature, 19th-century Literature and Romanticism, 20th-century Literature and Modernism

This conclusion argues that auto/biography is shadowed by the alter ego of scepticism, whether directed at the reality or intelligibility of selves; their representability; or the adequacy of the ...
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This conclusion argues that auto/biography is shadowed by the alter ego of scepticism, whether directed at the reality or intelligibility of selves; their representability; or the adequacy of the available forms of representation. It summarizes the resulting positions of anti‐subjectivity and autobiograficton, arguing that the sceptical engagements with life‐writing display a markedly performative dimension, using theoretical concepts from Judith Butler and Sidonie Smith. The notion of the performative reintroduces the ideas of fictionality and creativity to the heart of the autobiographic project; and to that extent could be said to inscribe even in formal autobiography some of the key qualities discovered here in more hybrid works, of ‘autobiografiction’ and imaginary writing. A literary autobiography's relation to a fictional oeuvre is discussed as working according to Derrida's logic of the supplement, with a comparable effect: posing autobiography as outside fiction, but infiltrating the autobiographical into the fiction, and thus reciprocally, the fictional into the autobiography. What such arguments bring out is how autobiography and fiction, while posed as mutually exclusive, are in fact profoundly interdependent, and constitute throughout the last two centuries a system of modern self‐representation which might itself be termed ‘autobiografiction’.Less

This conclusion argues that auto/biography is shadowed by the alter ego of scepticism, whether directed at the reality or intelligibility of selves; their representability; or the adequacy of the available forms of representation. It summarizes the resulting positions of anti‐subjectivity and autobiograficton, arguing that the sceptical engagements with life‐writing display a markedly performative dimension, using theoretical concepts from Judith Butler and Sidonie Smith. The notion of the performative reintroduces the ideas of fictionality and creativity to the heart of the autobiographic project; and to that extent could be said to inscribe even in formal autobiography some of the key qualities discovered here in more hybrid works, of ‘autobiografiction’ and imaginary writing. A literary autobiography's relation to a fictional oeuvre is discussed as working according to Derrida's logic of the supplement, with a comparable effect: posing autobiography as outside fiction, but infiltrating the autobiographical into the fiction, and thus reciprocally, the fictional into the autobiography. What such arguments bring out is how autobiography and fiction, while posed as mutually exclusive, are in fact profoundly interdependent, and constitute throughout the last two centuries a system of modern self‐representation which might itself be termed ‘autobiografiction’.

*James Oxley*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198566946
- eISBN:
- 9780191774904
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566946.003.0007
- Subject:
- Mathematics, Educational Mathematics

This chapter provides an overview of the basic questions associated with matroid representability and indicates how one actually goes about constructing representations. The key ideas are presented ...
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This chapter provides an overview of the basic questions associated with matroid representability and indicates how one actually goes about constructing representations. The key ideas are presented in Sections 6.1 and 6.3–6.6, which cover projective geometries, different matroid representations, constructing representations for matroids, representability over finite fields, and regular matroids, respectively. Section 6.2 looks at affine geometries, a class of highly symmetric structures that are closely linked to the projective geometries of Section 6.1. Section 6.7 discusses algebraic matroids, a class of matroids that properly contains the class of representable matroids and arises from algebraic dependence over a field. Section 6.8 focuses on characteristic sets, its main idea being concerned with how one can capture geometrically certain algebraic properties of a field. Section 6.9 examines modularity, a special property of flats that is important in several contexts including matroid constructions. Finally, Section 6.10 discusses an important class of matroids introduced by Dowling.Less

This chapter provides an overview of the basic questions associated with matroid representability and indicates how one actually goes about constructing representations. The key ideas are presented in Sections 6.1 and 6.3–6.6, which cover projective geometries, different matroid representations, constructing representations for matroids, representability over finite fields, and regular matroids, respectively. Section 6.2 looks at affine geometries, a class of highly symmetric structures that are closely linked to the projective geometries of Section 6.1. Section 6.7 discusses algebraic matroids, a class of matroids that properly contains the class of representable matroids and arises from algebraic dependence over a field. Section 6.8 focuses on characteristic sets, its main idea being concerned with how one can capture geometrically certain algebraic properties of a field. Section 6.9 examines modularity, a special property of flats that is important in several contexts including matroid constructions. Finally, Section 6.10 discusses an important class of matroids introduced by Dowling.

*James Oxley*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198566946
- eISBN:
- 9780191774904
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566946.003.0016
- Subject:
- Mathematics, Educational Mathematics

This chapter examines a number of unsolved problems. The discussions cover problems in linear representability; unimodal conjectures; critical problems; gammoids and transversal matroids; excluding a ...
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This chapter examines a number of unsolved problems. The discussions cover problems in linear representability; unimodal conjectures; critical problems; gammoids and transversal matroids; excluding a uniform matroid; and negatively correlated matroid.Less

This chapter examines a number of unsolved problems. The discussions cover problems in linear representability; unimodal conjectures; critical problems; gammoids and transversal matroids; excluding a uniform matroid; and negatively correlated matroid.

*Kai-Wen Lan*

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691156545
- eISBN:
- 9781400846016
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691156545.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter elaborates on the representability of the moduli problems defined in the previous chapter. The treatment here is biased towards the prorepresentability of local moduli and Artin's ...
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This chapter elaborates on the representability of the moduli problems defined in the previous chapter. The treatment here is biased towards the prorepresentability of local moduli and Artin's criterion of algebraic stacks. The geometric invariant theory or the theory of Barsotti–Tate groups has been set aside: the argument is very elementary and might be considered outdated by the experts in this area. The chapter, however, discusses the Kodaira–Spencer morphisms of abelian schemes with PEL structures, which are best understood via the study of deformation theory. It also considers the proof of the formal smoothness of local moduli functors, illustrating how the linear algebraic assumptions are used.Less

This chapter elaborates on the representability of the moduli problems defined in the previous chapter. The treatment here is biased towards the prorepresentability of local moduli and Artin's criterion of algebraic stacks. The geometric invariant theory or the theory of Barsotti–Tate groups has been set aside: the argument is very elementary and might be considered outdated by the experts in this area. The chapter, however, discusses the Kodaira–Spencer morphisms of abelian schemes with PEL structures, which are best understood via the study of deformation theory. It also considers the proof of the formal smoothness of local moduli functors, illustrating how the linear algebraic assumptions are used.