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Haupt-Kapovich Theorem Revisited.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Haupt-Kapovich Theorem Revisited./
Author:	Deev, Rodion N.
Description:	1 online resource (73 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28322375click for full text (PQDT)
ISBN:	9798534676327

Haupt-Kapovich Theorem Revisited.
Deev, Rodion N.

Haupt-Kapovich Theorem Revisited. - 1 online resource (73 pages)

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--New York University, 2021.

Includes bibliographical references

A theorem of O. Haupt, rediscovered by M. Kapovich and celebrated by his proof invoking Ratner theory, describes the set of de Rham cohomology classes on a topological orientable surface, which can be realized by an abelian differential in some respective complex structure, in purely topological terms. We give a simplification of Kapovich's proof and make an attempt to describe similarly pairs and triples of cohomology classes, which can be realized by abelian differentials in some complex structure. This leads to some interesting problems in algebraic geometry of curves, and gives an unexpected local description of the Teichmuller space.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798534676327Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Abelian surfacesIndex Terms--Genre/Form:

542853
Electronic books.

Haupt-Kapovich Theorem Revisited.
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245 1 0 $a Haupt-Kapovich Theorem Revisited.
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300 $a 1 online resource (73 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Bogomolov, Fedor A.
502 $a Thesis (Ph.D.)--New York University, 2021.
504 $a Includes bibliographical references
520 $a A theorem of O. Haupt, rediscovered by M. Kapovich and celebrated by his proof invoking Ratner theory, describes the set of de Rham cohomology classes on a topological orientable surface, which can be realized by an abelian differential in some respective complex structure, in purely topological terms. We give a simplification of Kapovich's proof and make an attempt to describe similarly pairs and triples of cohomology classes, which can be realized by abelian differentials in some complex structure. This leads to some interesting problems in algebraic geometry of curves, and gives an unexpected local description of the Teichmuller space.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Maps. $3 544078
650 4 $a Mapping. $3 3355992
650 4 $a Neighborhoods. $3 993475
653 $a Abelian surfaces
653 $a Riemannian surfaces
653 $a Teichmuller theory
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertations Abstracts International $g 83-02B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28322375 $z click for full text (PQDT)