scholarly journals Tropical geometry of moduli spaces of weighted stable curves

2015 ◽  
Vol 92 (2) ◽  
pp. 427-450 ◽  
Author(s):  
Martin Ulirsch
Keyword(s):  
Moduli Spaces ◽  
Tropical Geometry ◽  
Stable Curves

scholarly journals MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY

2016 ◽  
Vol 4 ◽  
Author(s):  
RENZO CAVALIERI ◽  
SIMON HAMPE ◽  
HANNAH MARKWIG ◽  
DHRUV RANGANATHAN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Tropical Geometry ◽  
Stable Curves ◽  
Tropical Curves ◽  
Graphic Matroid ◽  
Fibre Products ◽  
Algebraic Counterpart

We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector $w$ of weights, the moduli space of tropical $w$-stable curves can be given the structure of a balanced fan if and only if $w$ has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.

scholarly journals Modular compactifications of the space of pointed elliptic curves II

2011 ◽  
Vol 147 (6) ◽  
pp. 1843-1884 ◽  
Author(s):  
David Ishii Smyth
Keyword(s):  
Elliptic Curves ◽  
Moduli Spaces ◽  
Minimal Model ◽  
Model Program ◽  
Minimal Model Program ◽  
Stable Curves ◽  
Log Minimal Model Program

AbstractWe prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of Hassett’s log minimal model program for $\overline {M}_{1,n}$.

scholarly journals Moduli spaces of weighted pointed stable curves

2003 ◽  
Vol 173 (2) ◽  
pp. 316-352 ◽  
Author(s):  
Brendan Hassett
Keyword(s):  
Moduli Spaces ◽  
Stable Curves

scholarly journals The $${\mathcal {H}}$$-tautological ring

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Carl Lian
Keyword(s):  
Elliptic Curves ◽  
Moduli Spaces ◽  
General Setting ◽  
Rich Source ◽  
Stable Curves ◽  
Moduli Spaces Of Curves ◽  
Tautological Ring ◽  
Galois Covers ◽  
New Feature ◽  
New Framework

AbstractWe extend the theory of tautological classes on moduli spaces of stable curves to the more general setting of moduli spaces of admissible Galois covers of curves, introducing the so-called $${\mathcal {H}}$$ H -tautological ring. The main new feature is the existence of restriction-corestriction morphisms remembering intermediate quotients of Galois covers, which are a rich source of new classes. In particular, our new framework includes classes of Harris–Mumford admissible covers on moduli spaces of curves, which are known in some (and speculatively many more) examples to lie outside the usual tautological ring. We give additive generators for the $${\mathcal {H}}$$ H -tautological ring and show that their intersections may be algorithmically computed, building on work of Schmitt-van Zelm. As an application, we give a method for computing integrals of Harris-Mumford loci against tautological classes of complementary dimension, recovering and giving a mild generalization of a recent quasi-modularity result of the author for covers of elliptic curves.

Cycles in the moduli spaces of stable curves

2011 ◽  
pp. 565-608
Author(s):  
Enrico Arbarello ◽  
Maurizio Cornalba ◽  
Phillip A. Griffiths
Keyword(s):  
Moduli Spaces ◽  
Stable Curves
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