Stable Maps of Curves

Skeletons of stable maps II: superabundant geometries

We implement new techniques involving Artin fans to study the realizability of tropical stable maps in superabundant combinatorial types. Our approach is to understand the skeleton of a fundamental object in logarithmic Gromov–Witten theory—the stack of prestable maps to the Artin fan. This is used to examine the structure of the locus of realizable tropical curves and derive three principal co...

Contact Formulas for Rational Plane Curves via Stable Maps

Extending techniques of [4], we use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate certain characteristic numbers for rational plane curves. These characteristic numbers involve first-order (tangency) and second-order (inflectional) conditions. Although they may be virtual, they may be used as inputs in an enumeratively significan...

A pr 2 00 9 Abel maps for curves of compact type

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...

Quantitative analysis of thermo-mechanical behavior in 414 stainless steel using flow curves and processing maps

The hot deformation behavior of a typical martensitic stainless steel containing 2.1% Ni was investigated by means of the compression test in the strain rate range of 0.001-1 s-1 and temperature range of 950-1150 °C. The flow behavior of the steel was evaluated using the flow stress curves and flow softening map and by microstructural investigation. Taking into account of the strain effect on t...

Shortcut Node Classification for Membrane Residue Curve Maps

comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunov’s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour...

Relative Compactness and Product Stable Quotient Maps