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Liaison of Curves and Bundles.

Zhang, Mengyuan.

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Liaison of Curves and Bundles.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Liaison of Curves and Bundles./
作者:	Zhang, Mengyuan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	107 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Contained By:	Dissertations Abstracts International82-05B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27961146
ISBN:	9798678169938

Liaison of Curves and Bundles.
Zhang, Mengyuan.

Liaison of Curves and Bundles. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 107 p.

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2020.

This item must not be sold to any third party vendors.

This thesis is devoted to the study of two central objects in algebraic geometry - algebraic curves and vector bundles - through the unifying lens of liaison theory. The liaison theory of curves originated in the work of M. Noether in the late XIX century, and has since become an instrumental tool in the classification of space curves and the study of Hilbert schemes in general. In Chapter I, we develop a biliaison theory of sheaves and prove several main results in analogy to those from the liaison theory of codimension two subvarieties. In Chapter II, we use the liaison of curves on surfaces with ordinary singularities to prove multiple results about homological invariants of general projections of curves into projective three-space. In Chapter III, we apply biliaison of sheaves to the study of vector bundles. A general program is outlined to describe the moduli of bundles on a projective variety of irregularity zero through a stratification approach. We take the first steps by classifying bundles in the biliaison class of the zero sheaf on projective spaces and describing the moduli. In particular, our results give a description of the moduli of bundles on the projective plane.

ISBN: 9798678169938Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic Geometry

Liaison of Curves and Bundles.
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300 $a 107 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Eisenbud, David.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis is devoted to the study of two central objects in algebraic geometry - algebraic curves and vector bundles - through the unifying lens of liaison theory. The liaison theory of curves originated in the work of M. Noether in the late XIX century, and has since become an instrumental tool in the classification of space curves and the study of Hilbert schemes in general. In Chapter I, we develop a biliaison theory of sheaves and prove several main results in analogy to those from the liaison theory of codimension two subvarieties. In Chapter II, we use the liaison of curves on surfaces with ordinary singularities to prove multiple results about homological invariants of general projections of curves into projective three-space. In Chapter III, we apply biliaison of sheaves to the study of vector bundles. A general program is outlined to describe the moduli of bundles on a projective variety of irregularity zero through a stratification approach. We take the first steps by classifying bundles in the biliaison class of the zero sheaf on projective spaces and describing the moduli. In particular, our results give a description of the moduli of bundles on the projective plane.
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650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebraic Geometry
653 $a Bundles
653 $a Curves
653 $a Liaison
653 $a Moduli
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710 2 $a University of California, Berkeley. $b Mathematics. $3 1685396
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