ScholarLens Back to search
2012β€’Transactions of the American Mathematical SocietyOpen access

Birational contractions of \overline{𝑀}_{3,1} and \overline{𝑀}_{4,1}

David Jensen

Open full text 7 citations

Abstract

We study the birational geometry of M Β― 3 , 1 \overline {M}_{3,1} and M Β― 4 , 1 \overline {M}_{4,1} . In particular, we pose a pointed analogue of the Slope Conjecture and prove it in these low-genus cases. Using variation of GIT, we construct birational contractions of these spaces in which certain divisors of interest – the pointed Brill-Noether divisors – are contracted. As a consequence, we see that these pointed Brill-Noether divisors generate extremal rays of the effective cones for these spaces.

Open-access reader

About this research paper

What this paper is about

We study the birational geometry of M Β― 3 , 1 \overline {M}_{3,1} and M Β― 4 , 1 \overline {M}_{4,1} . In particular, we pose a pointed analogue of the Slope Conjecture and prove it in these low-genus cases. Using variation of GIT, we construct birational contractions of these spaces in which certain divisors of interest – the pointed Brill-Noether divisors – are contracted. As a consequence, we see that these pointed Brill-Noether divisors generate extremal rays of the effective cones for these spaces.

Why it matters

OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We study the birational geometry of M Β― 3 , 1 \overline {M}_{3,1} and M Β― 4 , 1 \overline {M}_{4,1} . In particular, we pose a pointed analogue of the Slope Conjecture and prove it in these low-genus cases. Using variation of GIT, we construct birational contractions of these spaces in which certain divisors of interest – the pointed Brill-Noether divisors – are contracted. As a consequence, we see that these pointed Brill-Noether divisors generate extremal rays of the effective cones for these spaces.

Key concepts: Overline, Mathematics, Particle physics, Physics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Birational contractions of \overline{𝑀}_{3,1} and \overline{𝑀}_{4,1} β€” Research Paper | ScholarLens