曲線模空間上的極小模型理論

Minimal Model Program for the Moduli Space of Stable Curves

劉宇翔(Yu-Hsiang Liu)

指導教授 ： 陳榮凱

國立臺灣大學/理學院/數學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.00504

摘要

本文的目標是探討Brendan Hassett、Donghoon Hyeon 和Yongnam
Lee 關於曲線模空間上的極小模型理論的工作。他們使用幾何不變理
論來描述了幾個曲線模空間Mg上的log canonical model，並給予它們
在模空間上的意義。

關鍵字

曲線模空間 ； 幾何不變理論 ； 極小模型理論

並列摘要

This paper aims to study B. Hassett, D. Hyeon and Y. Lee’s works on
log canonical models of Mg. They described certain log canonical models
Mg( ) of Mg via studying GIT of canonically embedded curves, and gave
their modular interpretations as compactifications of Mg.

並列關鍵字

moduli space of stable curves ； geometry invariant theory ； minimal model program.

參考文獻

[AFSW13] Jarod Alper, Maksym Fedorchuk, David Ishii Smyth, and Frederick van der Wyck, Log minimal model program for the moduli space of stable curves: The second flip. 2013.

[CMJL13] Sebastian Casalaina-Martin, David Jensen, and Radu Laza, Log canonical models and variation of GIT for genus four canonical curves. 2013.

[DM69] Pierre Deligne and David Mumford, The irreducibility of the space of curves of given genus. 1969.

[EH86] David Eisenbud and Joe Harris, Limit linear series: basic theory. 1986.

[Fab96] Carel Faber, Intersection-theoretical computations on Mg. 1996.