Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset U ⊂ S to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne-Mumford compactification is the unique, maximal AME compactification of the moduli space of curves. We also show ...

We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field ¥q2 whose number of ¥q2 -rational points reachs the Hasse-Weil upper bound. Under a hypothesis on non-gaps at rational points we prove that maximal curves are ¥q2 -isomorphic to y q + y = x for some m £ Z + . MIRAMARE TRIESTE March 1996 1 E-mail: [email protected] E-mail: f...

For every q = l with l a prime power greater than 2, the GK curve X is an Fq2 -maximal curve that is not Fq2 -covered by any Fq2 -maximal DeligneLusztig curve. Interestingly, X has a very large Fq2-automorphism group with respect to its genus. In this paper we compute the genera of a large variety of curves that are Galois-covered by the GK curve, thus providing several new values in the spectr...

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Very ample line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Bounds on global Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . 9 4. The degree of sub-maximal cu...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

We propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments [2]. Starting from results of discrete geometry [3, 4], the notion of maximal blurred segment of width ν [2] has been proposed, well adapted to possibly noisy curves. The f...

Previous results on genera g of Fq2 -maximal curves are improved: (1) Either g ≤ ⌊(q − q + 4)/6⌋ , or g = ⌊(q − 1)/4⌋ , or g = q(q − 1)/2 . (2) The hypothesis on the existence of a particular Weierstrass point in [2] is proved. (3) For q ≡ 1 (mod 3), q ≥ 13, no Fq2 -maximal curve of genus (q−1)(q−2)/3 exists. (4) For q ≡ 2 (mod 3), q ≥ 11, the non-singular Fq2 -model of the plane curve of equat...

The theory of boundedness classical operators real analyses on Morrey spaces defined Carleson curves has made significant progress in recent years as it allows for various applications. This study obtains new estimates about the maximal commutator operator $M_b$ and function $[M, b]$ curves.