Counting Lattice Points in Compactified Moduli Spaces of Curves
نویسندگان
چکیده
We define and count lattice points in the moduli spaceMg,n of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli spaceMg,n. The enumeration produces polynomials with top degree coefficients tautological intersection numbers onMg,n and constant term the orbifold Euler characteristic ofMg,n. We also prove a recursive formula which can be used to effectively calculate these polynomials.
منابع مشابه
String and Dilaton Equations for Counting Lattice Points in the Moduli Space of Curves
We prove that the Eynard-Orantin symplectic invariants of the curve xy − y2 = 1 are the orbifold Euler characteristics of the moduli spaces of genus g curves. We do this by associating to the Eynard-Orantin invariants of xy − y2 = 1 a problem of enumerating covers of the two-sphere branched over three points. This viewpoint produces new recursion relations—string and dilaton equations—between t...
متن کاملCompactified Moduli of Projective Bundles
We present a method for compactifying stacks of PGLn-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry natural virtual fundamental classes. We also prove a version of the Skolem-Noether theorem for certain algebra objects in the derived category, whi...
متن کاملIrreducible Cycles and Points in Special Position in Moduli Spaces for Tropical Curves
In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psiclasses and vital divisors are irreducible, and that locally irreducible divisors are also globally irreducible for n 6 6. In the second part of the paper, we show that the locus of point configurations in (R2)n in special position for co...
متن کاملCYCLIC COVERING MORPHISMS ON M0,n
We study cyclic covering morphisms from M0,n to moduli spaces of unpointed stable curves of positive genus or compactified moduli spaces of principally polarized abelian varieties. Our main application is a construction of new semipositive vector bundles and nef divisors on M0,n, with a view toward the F-conjecture. In particular, we construct new extremal rays of Nef(M0,n/Sn). We also find an ...
متن کاملGeometric Invariant Theory and Moduli Spaces of Pointed Curves
The main result of this dissertation is that Hilbert points parametrizing smooth curves with marked points are GIT-stable with respect to a wide range of linearizations. This is used to construct the coarse moduli spaces of stable weighted pointed curves Mg,A, including the moduli spaces Mg,n of Deligne-Mumford stable pointed curves, as well as ample line bundles on these spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010