اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn explicit solution to the weak Schottky problem
57
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus $g$, we write down a collection of polynomials in genus $g$ theta constants, such that their common zero locus contains the locus of Jacobians of genus $g$ curves as an irreducible component. These polynomials arise by applying a specific Schottky-Jung proportionality to an explicit collection of quartic identities for theta constants in genus $g-1$, which are suitable linear combinations of Riemanns quartic relations.
قيم البحث
اقرأ أيضاً
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.
All spacecraft attitude estimation methods are based on Wahbas optimization problem. This problem can be reduced to finding the largest eigenvalue and the corresponding eigenvector for Davenports $K$-matrix. Several iterative algorithms, such as QUES
T and FOMA, were proposed, aiming at reducing the computational cost. But their computational time is unpredictable because the iteration number is not fixed and the solution is not accurate in theory. Recently, an analytical solution, ESOQ was suggested. The advantages of analytical solutions are that their computational time is fixed and the solution should be accurate in theory if there is no numerical error. In this paper, we propose a different analytical solution to the Wahbas problem. We use simple and easy to be verified examples to show that this method is numerically more stable than ESOQ, potentially faster than QUEST and FOMA. We also use extensive simulation test to support this claim.
We construct a theory in which the solution to the strong CP problem is an emergent property of the background of the dark matter in the Universe. The role of the axion degree of freedom is played by multi-body collective excitations similar to spin-
waves in the medium of the dark matter of the Galactic halo. The dark matter is a vector particle whose low energy interactions with the Standard Model take the form of its spin density coupled to $G widetilde{G}$, which induces a potential on the average spin density inducing it to compensate $overline{theta}$, effectively removing CP violation in the strong sector in regions of the Universe with sufficient dark matter density. We discuss the viable parameter space, finding that light dark matter masses within a few orders of magnitude of the fuzzy limit are preferred, and discuss the associated signals with this type of solution to the strong CP problem.
We give a solution to the weak Schottky problem for genus five Jacobians with a vanishing theta null, answering a question of Grushevsky and Salvati Manni. More precisely, we show that if a principally polarized abelian variety of dimension five has
a vanishing theta null with a quadric tangent cone of rank at most three, then it is in the Jacobian locus, up to extra irreducible components. We employ a degeneration argument, together with a study of the ramification loci for the Gauss map of a theta divisor.
Because of its ineffectiveness, the usual arithmetic Hilbert-Samuel formula is not applicable in the context of Diophantine Approximation. In order to overcome this difficulty, the present paper presents explicit estimates for arithmetic Hilbert Functions of closed subvarieties in projective space.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
