共查询到20条相似文献,搜索用时 0 毫秒
1.
Thomas Keilen 《Transactions of the American Mathematical Society》2005,357(6):2467-2481
Francesco Severi (1921) showed that equisingular families of plane nodal curves are T-smooth, i.e. smooth of the expected dimension, whenever they are non-empty. For families with more complicated singularities this is no longer true. Given a divisor on a smooth projective surface it thus makes sense to look for conditions which ensure that the family of irreducible curves in the linear system with precisely singular points of types is T-smooth. Considering different surfaces including the projective plane, general surfaces in , products of curves and geometrically ruled surfaces, we produce a sufficient condition of the type
where is some invariant of the singularity type and is some constant. This generalises the results of Greuel, Lossen, and Shustin (2001) for the plane case, combining their methods and the method of Bogomolov instability. For many singularity types the -invariant leads to essentially better conditions than the invariants used by Greuel, Lossen, and Shustin (1997), and for most classes of geometrically ruled surfaces our results are the first known for T-smoothness at all.
where is some invariant of the singularity type and is some constant. This generalises the results of Greuel, Lossen, and Shustin (2001) for the plane case, combining their methods and the method of Bogomolov instability. For many singularity types the -invariant leads to essentially better conditions than the invariants used by Greuel, Lossen, and Shustin (1997), and for most classes of geometrically ruled surfaces our results are the first known for T-smoothness at all.
2.
Throughout this paper we study the existence of irreducible curves on smooth projective surfaces with singular points of prescribed topological types . There are necessary conditions for the existence of the type for some fixed divisor on and suitable coefficients , and , and the main sufficient condition that we find is of the same type, saying it is asymptotically proper. Ten years ago general results of this quality were not known even for the case . An important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up of the form , deduced from the Kawamata-Vieweg Vanishing Theorem. Its proof covers the first part of the paper, while the middle part is devoted to the existence theorems. In the last part we investigate our conditions on ruled surfaces, products of elliptic curves, surfaces in , and K3-surfaces.
3.
Summary We consider flat families of reduced curves on a smooth surfaceS such that each memberC has the same number of singularities and each singularity has a fixed singularity type (up to analytic resp. topological
equivalence). We show that these families are represented by a schemeH and give sufficient conditions for the smoothness ofH (atC). Our results improve previously known criteria for families with fixed analytic singularity type and seem to be quite sharp
for curves in ℙ2 of small degree. Moreover, for families with fixed topological type this paper seems to be the first in which arbitrary singularities
are treated.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
4.
We compute the number of rational degree d plane curves having prescribed fixed and moving contacts to a smooth plane cubic E. We use twisted stable maps to the stack for r large, where is the rth root of along E. We prove that certain Gromov–Witten invariants of this stack are enumerative, and establish recursive formulas for these numbers. 相似文献
5.
Jian Kong 《Transactions of the American Mathematical Society》2003,355(8):3175-3180
We compute the Seshadri constants on the Jacobian of hyperelliptic curves, as well as of curves with genus three and four. For higher genus curves we conclude that if the Seshadri constants of their Jacobian are less than 2, then the curves must be hyperelliptic.
6.
7.
8.
9.
P. G. Walsh. 《Mathematics of Computation》2000,69(231):1183-1191
The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in , the ring of polynomials with coefficients from the field of Laurent series in with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complexity bound for the number of bit operations required to perform this irreducibility test is computed.
10.
This paper discusses a theorem in birational geometry that J.L. Coolidge attributed to Alfred Clebsch. The background is reconstructed from letters Felix Klein exchanged with Max Noether in 1894, when Noether was completing work on a lengthy report with Alexander Brill on the history of algebraic functions. Noether was deeply troubled to learn that Klein had informed him back in 1869 about relevant results that Clebsch and Leopold Kronecker had discussed in Berlin. These exchanges with Klein led to revisions in the Brill-Noether report, made in part to ensure Noether's own priority rights and larger intellectual legacy. 相似文献
11.
A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set
of the Desarguesian plane PG(2,q) is obtained. The case where
is a maximal (k,n)-arc is considered in greater depth.
Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni. 相似文献
12.
We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which every slope semistable sheaf yields a Bridgeland semistable object of maximal phase. Then, we study tilt stability as the polarization ω gets large, and give sufficient conditions for tilt-stability of sheaves of the following two forms: 1) twists of ideal sheaves or 2) torsion-free sheaves whose first Chern class is twice a minimum possible value. 相似文献
13.
Nikolai Durov introduced the theory of generalized rings and schemes to study Arakelov geometry in an alternative algebraic framework, and introduced the residue field at the infinite place, 𝔽∞. We show an elementary algebraic approach to modules and algebras over this object, define prime congruences, show that the polynomial ring of n variables is of Krull dimension n, and derive a prime decomposition theorem for these primes. 相似文献
14.
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds, analyse the complexity of the algorithm and provide a complete implementation. 相似文献
15.
16.
This paper explores homological mirror symmetry for weighted blowups of toric varietes. It will be shown that both the A-model and B-model categories have natural semi-orthogonal decompositions. An explicit equivalence of the right orthogonal categories will be shown for the case of toric surfaces. 相似文献
17.
Let X be a set of order n and Y be a set of order m. An (n,m,{w
1, w
2})-separating hash family is a set
of N functions from X to Y such that for any
with
, |X
1| = w
1 and |X
2| = w
2, there exists an element
such that
. In this paper, we provide explicit constructions of separating hash families using algebraic curves over finite fields. In particular, applying the Garcia–Stichtenoth curves, we obtain an infinite class of explicitly constructed (n,m,{w
1,w
2})–separating hash families with
for fixed m, w
1, and w
2. Similar results for strong separating hash families are also obtained. As consequences of our main results, we present explicit constructions of infinite classes of frameproof codes, secure frameproof codes and identifiable parent property codes with length
where n is the size of the codes. In fact, all the above explicit constructions of hash families and codes provide the best asymptotic behavior achieving the bound
, which substantially improve the results in [
8, 15, 17] give an answer to the fifth open problem presented in [11]. 相似文献
18.
Zhi Jiang 《manuscripta mathematica》2007,124(2):173-182
In this paper the author improved a proposition of Sommese on the restriction of holomorphic forms. By studying several examples,
it turns out that this improvement is more or less optimal. 相似文献
19.
In this paper, we use character-theoretic techniques to give new nonexistence results for -strong external difference families (SEDFs). We also use cyclotomic classes to give two new classes of SEDFs with . 相似文献
20.
We will give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. 相似文献