Abstract/Details

Stability manifolds of P(1) and Calabi-Yau surfaces


2006 2006

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Abstract (summary)

The notion of stability conditions on triangulated categories was formulated in [15]. It organizes certain bounded t-structures on a triangulated category into a complex manifold.

We will describe the stability manifold of the bounded derived category D([special characters omitted]) of coherent sheaves on [special characters omitted], denoted by Stab(D([special characters omitted])). This part of the work has been published in [32].

After preparation on spectral sequences and n-Calabi-Yau categories , we will concentrate on stability conditions on 2-Calabi-Yau categories. Our main result here is the connectedness of stability manifolds of the cotangent bundle of [special characters omitted] and abelian surfaces. This completes Bridgeland's work on the description of these manifolds.

Stability conditions have been studied for one-dimensional spaces in [15], [23], [32], [28], and [17], higher-dimensional spaces in [35], [14], [16], [12], [13], [28], [29], [2], [36], [24], [7], and [1], and A-categories in [35], [34], [37], and [26]. The stability manifold of the category [special characters omitted] for sl2 has been computed in [30]. Some general aspects have been studied in [2] and [23].

The author recommends [11], [3, Section 0.6] and [20], [19], [21] for introductions and the original physical motivation to this subject. Notation of derived categories is mainly based on [22].

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Algebraic geometry; Calabi-Yau surfaces; Derived categories; Stability manifolds
Title
Stability manifolds of P(1) and Calabi-Yau surfaces
Author
Okada, So
Number of pages
43
Publication year
2006
Degree date
2006
School code
0118
Source
DAI-B 67/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542982231
Advisor
Mirkovic, Ivan
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3242109
ProQuest document ID
305302727
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305302727
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