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Interpolation and vector bundles on ...

Harvard University.

Interpolation and vector bundles on curves.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Interpolation and vector bundles on curves./
Author:	Atanasov, Atanas Valeryev.
Description:	1 online resource (100 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
Contained By:	Dissertation Abstracts International77-04B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781339291666

Interpolation and vector bundles on curves.
Atanasov, Atanas Valeryev.

Interpolation and vector bundles on curves. - 1 online resource (100 pages)

Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.

Thesis (Ph.D.)--Harvard University, 2015.

Includes bibliographical references

Interpolation is a property of vector bundles on curves closely related to slope stability. The notion is motivated by the deformation theory of curves in projective space incident to given fixed subvarieties. If the normal bundle of a projective curve satisfies interpolation, then curves in the same component of the Hilbert scheme exhibit normal behavior with respect to incident problems.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781339291666Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Interpolation and vector bundles on curves.
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008 190606s2015 xx obm 000 0 eng d
020 $a 9781339291666
035 $a (MiAaPQ)AAI3738687
035 $a (MiAaPQ)vireo:harvard279Atanasov
035 $a AAI3738687
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Atanasov, Atanas Valeryev. $3 1193163
245 1 0 $a Interpolation and vector bundles on curves.
264 0 $c 2015
300 $a 1 online resource (100 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
500 $a Adviser: Joe Harris.
502 $a Thesis (Ph.D.)--Harvard University, 2015.
504 $a Includes bibliographical references
520 $a Interpolation is a property of vector bundles on curves closely related to slope stability. The notion is motivated by the deformation theory of curves in projective space incident to given fixed subvarieties. If the normal bundle of a projective curve satisfies interpolation, then curves in the same component of the Hilbert scheme exhibit normal behavior with respect to incident problems.
520 $a We demonstrate how to use degeneration arguments to deduce interpolation. In particular, we show that a general connected space curve of degree d and genus g satisfies interpolation for d >= g+3 unless d = 5 and g = 2. As a second application, we show that a general elliptic curve of degree d in P.
520 $a nsatisfies a slightly weaker notion when d >= 7, d >= n+1, and the remainder of 2d modulo n-1 lies between 3 and n-2 inclusive. We also show that interpolation is equivalent to the---a priori stricter---notion of strong interpolation.
520 $a The use of degeneration techniques to prove interpolation requires working with modifications of vector bundles. In the second part of this thesis, we develop a general theory of modifications for bundles over varieties of arbitrary dimensions. We explain how to apply this machinery when dealing with families of curves, and prove a number of results which allow us to deduce interpolation via short exact sequences.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Harvard University. $b Mathematics. $3 1193029
773 0 $t Dissertation Abstracts International $g 77-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3738687 $z click for full text (PQDT)

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