Birational geometry of genus one fibrations and stability of pencils of plane curves / Aline Zanardini.

Format:

Book

Thesis/Dissertation

Author/Creator:

Zanardini, Aline, author.

Contributor:

Grassi, Antonella, degree supervisor.

University of Pennsylvania. Department of Mathematics, degree granting institution.

Language:

English

Subjects (All):

Mathematics.

Theoretical mathematics.

Applied mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Local Subjects:

Mathematics.

Theoretical mathematics.

Applied mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Genre:

Academic theses.

Physical Description:

1 online resource (233 pages)

Contained In:

Dissertations Abstracts International 82-11B.

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2021.

Language Note:

English

System Details:

Mode of access: World Wide Web.

text file

Summary:

In the first part of this thesis we give a complete classification of relative log canonical models for genus one fibrations in dimensions two and three. More concretely, we generalize the work in [2] by considering both (i) the case where it is not assumed the existence of a section, but of a multisection instead; and (ii) the case of threefolds in one dimension higher. In the second part, we investigate the stability of pencils of plane curves in the sense of geometric invariant theory. One of our main results relates the stability of a pencil of plane curves P to the log canonical threshold of pairs (P.

2,C_d), where C_d is a curve in P, thus extending an idea of Hacking [23] and Kim-Lee [27]. Part of our approach consists in observing that we can sometimes determine whether a pencil P is (semi)stable or not by looking at the stability of the curves lying on it. As a beautiful application, we completely describe the stability of Halphen pencils of index two -- classical geometric objects first introduced by Halphen in 1882 [24]. Inspired by the work of Miranda in [40], we provide explicit stability criteria in terms of the geometry of their associated rational elliptic surfaces.

Notes:

Source: Dissertations Abstracts International, Volume: 82-11, Section: B.

Advisors: Grassi, Antonella; Committee members: Tony Pantev; Wolfgang Ziller.

Department: Mathematics.

Ph.D. University of Pennsylvania 2021.

Local Notes:

School code: 0175

ISBN:

9798738617645

Access Restriction:

Restricted for use by site license.

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