Moduli of curves

TL;DR: A degeneration of a singular curve on a toric surface, called a tropicalization, was constructed by E. Shustin this paper, who defined a tropical version of a 1-tacnodal curve, that is, a curve having exactly one singular point whose topological type is $A_3.

TL;DR: In this paper , the effective cones of higher codimension classes were investigated and it was shown that a large collection of boundary strata of rational tails type are extremal in their effective cones on M g , n and provided evidence for the conjecture that all boundarystrata of M g, n were extremal.

TL;DR: In this paper, a new approach to study Koszul cohomology of general g ds on general curves via degenerations and deformations was proposed. And the authors proved projective normality for general line bundles with h(L) ≤ 1.

TL;DR: In this article, the authors generalize this result to stable curves of higher gonality having two smooth components and one node, and for trigonal stable curves with two smooth non-rational components and any number of nodes.

TL;DR: In this article, the authors define a parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J).

TL;DR: Weyl as discussed by the authors discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations using basic concepts from algebra, and examines the various properties of the groups.

TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).