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The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces./
Author:	Stapleton, David.
Description:	1 online resource (63 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.
Contained By:	Dissertation Abstracts International79-03B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355470659

The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces.
Stapleton, David.

The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces. - 1 online resource (63 pages)

Source: Dissertation Abstracts International, Volume: 79-03(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

The degree of irrationality of an n-dimensional algebraic variety X is the minimal degree of a rational map from X to Pn. The degree of irrationality is a birational invariant with the purpose of measuring how far X is from being rational. For example the degree of irrationality of X is 1 if and only if X is rational. While the invariant has a very classical appearance, it has not attracted very much attention until very recently in [BDPE+15] where it was shown that the degree of irrationality of a very general degree d hypersurface in Pn+1 is d -- 1, if d is sufficiently large. The method of proof involves relating the geometry of a low degree map to projective space to the geometry of lines in projective space. In this dissertation we show that these methods can be extended to compute the degree of irrationality of hypersurfaces in other rational homogeneous spaces: quadrics, Grassmannians, and products of projective spaces. In particular, we relate the geometry of low degree maps from hypersurfaces in these rational homogeneous spaces to the geometry of lines inside these rational homegeneous spaces. These computations represent some of the first computations of the degree of irrationality for higher dimensional varieties.

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

Mode of access: World Wide Web

ISBN: 9780355470659Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Stapleton, David. $3 1180835
245 1 4 $a The Degree of Irrationality of Very General Hypersurfaces in Some Homogeneous Spaces.
264 0 $c 2017
300 $a 1 online resource (63 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: 79-03(E), Section: B.
500 $a Adviser: Robert K. Lazarsfeld.
502 $a Thesis (Ph.D.) $c State University of New York at Stony Brook $d 2017.
504 $a Includes bibliographical references
520 $a The degree of irrationality of an n-dimensional algebraic variety X is the minimal degree of a rational map from X to Pn. The degree of irrationality is a birational invariant with the purpose of measuring how far X is from being rational. For example the degree of irrationality of X is 1 if and only if X is rational. While the invariant has a very classical appearance, it has not attracted very much attention until very recently in [BDPE+15] where it was shown that the degree of irrationality of a very general degree d hypersurface in Pn+1 is d -- 1, if d is sufficiently large. The method of proof involves relating the geometry of a low degree map to projective space to the geometry of lines in projective space. In this dissertation we show that these methods can be extended to compute the degree of irrationality of hypersurfaces in other rational homogeneous spaces: quadrics, Grassmannians, and products of projective spaces. In particular, we relate the geometry of low degree maps from hypersurfaces in these rational homogeneous spaces to the geometry of lines inside these rational homegeneous spaces. These computations represent some of the first computations of the degree of irrationality for higher dimensional varieties.
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 State University of New York at Stony Brook. $b Mathematics. $3 1180836
773 0 $t Dissertation Abstracts International $g 79-03B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10601029 $z click for full text (PQDT)