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thesis-final.pdf (317.24 KB)
ETD Abstract Container
Abstract Header
Vector Bundles and Projective Varieties
Author Info
Marino, Nicholas John
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018
Abstract Details
Year and Degree
2019, Master of Sciences, Case Western Reserve University, Mathematics.
Abstract
Vector bundles play a prominent role in the study of projective algebraic varieties. Vector bundles can describe facets of the intrinsic geometry of a variety, as well as its relationship to other varieties, especially projective spaces. Additionally, being among the simplest examples of coherent sheaves, they can be manipulated by a wealth of technical machinery. Here we outline the general theory of vector bundles and describe their classification and structure. We also consider some special bundles and general results in low dimensions, especially rank 2 bundles and surfaces, as well as bundles on projective spaces. Finally, we indicate some open problems and current areas of research.
Committee
Nick Gurski (Committee Chair)
David Singer (Committee Member)
Joel Langer (Committee Member)
Pages
54 p.
Subject Headings
Mathematics
Keywords
algebraic geometry
;
vector bundles
;
projective geometry
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Citations
Marino, N. J. (2019).
Vector Bundles and Projective Varieties
[Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018
APA Style (7th edition)
Marino, Nicholas.
Vector Bundles and Projective Varieties.
2019. Case Western Reserve University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018.
MLA Style (8th edition)
Marino, Nicholas. "Vector Bundles and Projective Varieties." Master's thesis, Case Western Reserve University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018
Chicago Manual of Style (17th edition)
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Document number:
case1544457943307018
Download Count:
2,456
Copyright Info
© 2018, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.