Log minimal model program for the moduli space of stable curves of genus three

By Donghoon Hyeon, Yongnam Lee. 2007

69 citations recorded by the source corpus.

We completely carry out the log minimal model program for the moduli space of stable curves of genus three with respect to the total boundary $\delta$: We give a modular interpretation of the log canonical model for the pair $(\bar{\mathcal M}_3, \a\d)$ for each $\a \in [0,7/10)$ and of the birational maps between them. By using the modular description, we are able to identify all but one log canonical models $\Mg(\a)$, $\a \in [0,1]$, with existing compactifications of $M_3$, some new and others classical, while the exception gives a new modular compactification of $M_3$.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc0dc24b0988b32bdbc69ff01d3e825d55bb16e9

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In Geometry and Topology

1. Y. Odaka
2. D. Smyth
3. Cristiano Spotti
4. Song Sun
5. Maksym Fedorchuk
6. Jarod Alper
7. Chenyang Xu
8. Donghoon Hyeon

In Mathematical Physics

1. D. Smyth
2. Song Sun
3. Maksym Fedorchuk
4. Cristiano Spotti
5. Jarod Alper
6. Donghoon Hyeon
7. Y. Odaka
8. Brendan Hassett

Citations in the corpus

• Log minimal model program for the moduli space of stable curves: The first flip (2008, background): “When g =3, a bicanonical h-semistable curve is Hilbert strictly semistable if and only if it has a tacnode [ HL07a ].”
• Good Moduli Spaces for Artin Stacks (2008, background): “Hassett and Hyeon show in [14] for g > 4 (the g = 3 case is handled in [17]) that a flip occurs at the next step in the log minimal model program at α = 7/10.”
• Alternate Compactifications of Moduli Spaces of Curves (2010, methodology): “ contracts the locus of the elliptic bridges to a point, and is an isomorphism elsewhere. 4Since M3 is mildly singular, it is not completely obvious that (M3; 9 11 ) is a klt pair; this is veried in [HL10]. In order to simplify exposition, we will omit standard discrepancy calculations needed to jus”
• Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics (2012, methodology): “What are the modular interpretations via log Del Pezzo surfaces for each step of the Hassett-Keel program in [29]? In addition, are there also stability interpretations for them?”