Some 4-point Hurwitz Numbers in Positive Characteristic
نویسندگان
چکیده
In this paper, we compute the number of covers of the projective line with given ramification in two related families of examples. We are able to conclude that for a particular choice of degeneration, all covers in these families degenerate to separable (admissible) covers. Starting from a good understanding of the complex case, the proof is centered on the theory of stable reduction of Galois covers.
منابع مشابه
Reduction of covers and Hurwitz spaces
In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion for good reduction for covers of the projective line branched at three points. We use the ideas of Raynaud to study the case of covers of the projective line branched at four points. Under some condition o...
متن کاملExtremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
We study correlation functions of single-cycle chiral operators in Sym T 4, the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields are single-valued. We compute some simple four-point functions and study how the sum over inequivalent branched covering maps splits under OPEs. We ...
متن کاملSpin Hurwitz Numbers and the Gromov-Witten Invariants of Kähler Surfaces
The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These “spin Hurwitz numbers”, recently studied by Eskin, Okounkov and Pandharipande, are interesting in their own right. By the authors’ previous work, they are also related to the Gromov-Witten invariants of Kähler surfaces. We prove a recursive formula f...
متن کاملThe Gromov-witten Potential of a Point, Hurwitz Numbers, and Hodge Integrals
Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permutations into transpositions), have been extensively studied for over a century. The Gromov-Witten potential F of a point, the generating series for Hodge integrals on the moduli space of curves, has been a central object of study in Gromov-Witten theory. We define a slightly enriched Gro...
متن کاملRamifications of Hurwitz theory, KP integrability and quantum curves
In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.
متن کامل