Lectures on Tropical Curves and Their Moduli Spaces
نویسنده
چکیده
These are notes for a series of five lectures on “Moduli and degenerations of algebraic curves via tropical geometry” delivered at the CIMPA-CIMAT-ICTP School on Moduli of Curves, February 29-March 4, 2016 in Guanajuato, Mexico.
منابع مشابه
An introduction to moduli spaces of curves and its intersection theory
The material of this chapter is based on a series of three lectures for graduate students that the author gave at the Journées mathématiques de Glanon in July 2006. We introduce moduli spaces of smooth and stable curves, the tautological cohomology classes on these spaces, and explain how to compute all possible intersection numbers between these classes.
متن کاملAlgebraic and tropical curves: comparing their moduli spaces
We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its bordification given by weighted tropical curves, and its compactification by extended (weighted) tropical curves. We compare it to the moduli spaces of smooth and stable, n-pointed algebraic curves, from the combinatorial, the topological, and the Teichmüller point of view.
متن کاملTropical Orbit Spaces and the Moduli Spaces of Elliptic Tropical Curves
We give a definition of tropical orbit spaces and their morphisms. We show that, under certain conditions, the weighted number of preimages of a point in the target of such a morphism does not depend on the choice of this point. We equip the moduli spaces of elliptic tropical curves with a structure of tropical orbit space and, using our results on tropical orbit spaces, simplify the known proo...
متن کاملTropical Fans and the Moduli Spaces of Tropical Curves
We give a rigorous definition of tropical fans (the “local building blocks for tropical varieties”) and their morphisms. For a morphism of tropical fans of the same dimension we show that the number of inverse images (counted with suitable tropical multiplicities) of a point in the target does not depend on the chosen point — a statement that can be viewed as one of the important first steps of...
متن کاملLectures on Moduli Spaces of Elliptic Curves
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. 1 Their goal is to introduce and motivate basic concepts and constructions important in the study of moduli spaces of curves and abelian varieties through the example of elliptic curves. The advantage of working with elliptic curves is that most constructio...
متن کامل