ترغب بنشر مسار تعليمي؟ اضغط هنا

Some 4-point Hurwitz numbers in positive characteristic

190   0   0.0 ( 0 )
 نشر من قبل Brian Osserman
 تاريخ النشر 2009
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p. Our techniques involve related computations in the case of three branch points, and allow us to conclude in many cases that for a particular choice of degeneration, all the covers we consider degenerate to separable (admissible) covers. Starting from a good understanding of the complex case, the proof is centered on the theory of stable reduction of Galois covers.



قيم البحث

اقرأ أيضاً

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X is simply c onnected while pi_1(M) = (Z/3)^2. In characteristic 3, we find that X and M have different Hodge numbers, which would be impossible in characteristic 0. In an appendix, we give a streamlined proof of Abuafs result that the ring H^*(O) is a derived invariant of complex threefolds and fourfolds. A second appendix by Alexander Petrov gives a family of higher-dimensional examples to show that h^{0,3} is not a derived invariant in any positive characteristic.
173 - Irene I. Bouw 2007
We study the existence of Fuchsian differential equations in positive characteristic with nilpotent p-curvature, and given local invariants. In the case of differential equations with logarithmic local mononodromy, we determine the minimal possible degree of a polynomial solution.
We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines branched at 4 points and obtain information on the s tructure of the Hurwitz curve parametrizing these covers.
104 - Daniel Bragg , Ziquan Yang 2021
We study isogenies between K3 surfaces in positive characteristic. Our main result is a characterization of K3 surfaces isogenous to a given K3 surface $X$ in terms of certain integral sublattices of the second rational $ell$-adic and crystalline coh omology groups of $X$. This is a positive characteristic analog of a result of Huybrechts, and extends results of the second author. We give applications to the reduction types of K3 surfaces and to the surjectivity of the period morphism. To prove these results we describe a theory of B-fields and Mukai lattices in positive characteristic, which may be of independent interest. We also prove some results on lifting twisted Fourier--Mukai equivalences to characteristic 0, generalizing results of Lieblich and Olsson.
103 - Thang Pham , Le Anh Vinh 2019
Let $mathbb{F}_q$ be an arbitrary finite field, and $mathcal{E}$ be a set of points in $mathbb{F}_q^d$. Let $Delta(mathcal{E})$ be the set of distances determined by pairs of points in $mathcal{E}$. By using the Kloosterman sums, Iosevich and Rudnev proved that if $|mathcal{E}|ge 4q^{frac{d+1}{2}}$, then $Delta(mathcal{E})=mathbb{F}_q$. In general, this result is sharp in odd-dimensional spaces over arbitrary finite fields. In this paper, we use the recent point-plane incidence bound due to Rudnev to prove that if $mathcal{E}$ has Cartesian product structure in vector spaces over prime fields, then we can break the exponent $(d+1)/2$, and still cover all distances. We also show that the number of pairs of points in $mathcal{E}$ of any given distance is close to its expected value.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا