Geometry of Meromorphic Functions and Intersections on Moduli Spaces of Curves
نویسنده
چکیده
In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. And then we obtain an algorithm expressing intersection numbers 〈τn,m ∏r−1 i=1 τ ki 0,i〉g via correlation functions of primaries.
منابع مشابه
Intersections of Tautological Classes on Blowups of Moduli Spaces of Genus-One Curves
We give two recursions for computing top intersections of tautological classes on blowups of moduli spaces of genus-one curves. One of these recursions is analogous to the well-known string equation. As shown in previous papers, these numbers are useful for computing genusone enumerative invariants of projective spaces and Gromov-Witten invariants of complete intersections.
متن کاملComposition operators and natural metrics in meromorphic function classes $Q_p$
In this paper, we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes. Also, these classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...
متن کاملNon - Critical Strings , Del Pezzo Singularities and Seiberg – Witten Curves
We study limits of four-dimensional type II Calabi–Yau compactifications with vanishing four-cycle singularities, which are dual to T 2 compactifications of the six-dimensional non-critical string with E 8 symmetry. We define proper sub-sectors of the full string theory, which can be consistently decoupled. In this way we obtain rigid effective theories that have an intrinsically stringy BPS sp...
متن کاملDegenerations of Abelian Differentials
Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, give dimension bounds for their moduli spaces, and establish smoothability criteria. As applications, we show that the spin parity of holomorphic...
متن کاملNew results of intersection numbers on moduli spaces of curves.
We present a series of results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's tau classes, an effective recursion formula to compute higher Weil-Petersson volumes, several new recursion formulae of intersection numbers and our proof of a conjecture of Itzykson and Zuber conc...
متن کامل