In this paper, we study combinatorial properties of stable curves. To the dual graph of any nodal curve, there is naturally associated a group, which is the group of components of the Néron model of the generalized Jacobian of the curve. We study the order of this group, called the complexity. In particular, we provide a partial characterization of the stable curves having maximal complexity, and we provide an upper bound, depending only on the genus g of the curve, on the maximal complexity of stable curves; this bound is asymptotically sharp for g ≫ 0. Eventually, we state some conjectures on the behavior of stable curves with maximal complexity, and prove partial results in this direction. © de Gruyter 2011.
Busonero, S., MASCARENHAS MELO, A.M., Stoppino, L. (2011). On the complexity group of stable curves. ADVANCES IN GEOMETRY, 11(2), 241-272 [10.1515/ADVGEOM.2011.004].
On the complexity group of stable curves
MASCARENHAS MELO, ANA MARGARIDA;STOPPINO, LIDIA
2011-01-01
Abstract
In this paper, we study combinatorial properties of stable curves. To the dual graph of any nodal curve, there is naturally associated a group, which is the group of components of the Néron model of the generalized Jacobian of the curve. We study the order of this group, called the complexity. In particular, we provide a partial characterization of the stable curves having maximal complexity, and we provide an upper bound, depending only on the genus g of the curve, on the maximal complexity of stable curves; this bound is asymptotically sharp for g ≫ 0. Eventually, we state some conjectures on the behavior of stable curves with maximal complexity, and prove partial results in this direction. © de Gruyter 2011.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
