Search

We consider the loci of curves of genus 2 and 3 admitting a |$d$| -to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow classes, recovering results of Faber–Pagani and van Zelm when |$d=2$|⁠. The answers exhibit quasimodularity properties similar to those in the Gromov–Witten theory of a fixed genus 1 curve; we conjecture that the quasimodularity persists in higher genus and indicate a number of possible variants. [ABSTRACT FROM AUTHOR]

Let X → ℙ1 be a general cyclic cover. We give a simple formula for the number of equivariant meromorphic functions on X subject to ramification conditions at variable points. This generalizes and gives a new proof of a recent result of the second author and Pirola on hyperelliptic odd covers. [ABSTRACT FROM AUTHOR]

We show that various loci of stable curves of sufficiently large genus admitting degree d covers of positive genus curves define non-tautological algebraic cycles on M ¯ g , N , assuming the non-vanishing of the d-th Fourier coefficient of a certain modular form. Our results build on those of Graber-Pandharipande and van Zelm for degree 2 covers of elliptic curves; the main new ingredient is a method to intersect the cycles in question with boundary strata, as developed recently by Schmitt-van Zelm and the author. [ABSTRACT FROM AUTHOR]

We 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 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 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. [ABSTRACT FROM AUTHOR]

We consider the loci of curves of genus 2 and 3 admitting a |$d$| -to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow classes, recovering results of Faber–Pagani and van Zelm when |$d=2$|⁠. The answers exhibit quasimodularity properties similar to those in the Gromov–Witten theory of a fixed genus 1 curve; we conjecture that the quasimodularity persists in higher genus and indicate a number of possible variants. [ABSTRACT FROM AUTHOR]

This article characterizes anticipated changes in fleet structure, vessel harvesting activity, and economic performance in the Pacific Coast groundfish fishery under an individual fishing quota management program. Results suggest that the current fleet of 117 vessels will be reduced by roughly 50%--66% to 40--60 vessels, resulting in annual cost savings of $18--$22 million (based on 2004 price and cost estimates). However, cost savings could be significantly less if restrictions on quota trading across vessels are incorporated into the program design. Alternative modes of collecting fees to fund program administration and their impact on fleet size and total fishery value are also studied. We conclude that a program of individual fishing quotas, if carefully designed, can be an attractive alternative for management of the Pacific Coast groundfish fishery. [ABSTRACT FROM AUTHOR]