We give a description of the tropical Severi variety of univariate polynomials of degree n having two double roots. We show that, as a set, it is given as the union of three explicit types of cones of maximal dimension n − 1, where only cones of two of these types are cones of the secondary fan of {0, . . . , n}. Through Kapranov’s theorem, this goal is achieved by a careful study of the possib...

ضرورت دسترسی به کاربردهای وسیع تصاویر ابرطیفی سبب توسعة سیستم‌های تصویربرداری نوآورانه و اقتصادی در ثبت این شده است. به‌منظور استفاده از تصاویر، لازم است ارتباط هندسی دقیقی میان آنها فضای زمین برقرار شود فرایند نیازمند نقاط کنترلی بسیاری نکته راهکارهای اصلاح منطبق با ساختار هریک دوربین‌ها را بارز می‌کند. سنجندة (nm 400-1000) BaySpec OCI-F یکی نوآورانه‌ای که هندسة پوش‌بروم دریافت سنجنده، علاوه‌ب...

For a smooth surface S in P 3 of degree d and for positive integers n, δ, the Severi variety V 0 n,δ (S) is the subvariety of the linear system |O S (n)| which parametrizes curves with δ nodes. We show that for S general, n ≥ d and for all δ with 0 ≤ δ ≤ dim(|O S (n)|), then V 0 n,δ (S) has at least one component which is reduced, of the expected dimension dim(|O S (n)|) − δ. We also construct ...

In this paper, we generalize a result of Karpenko on the torsion in the second quotient of the gamma filtration for Severi-Brauer varieties to higher degrees. As an application, we provide a nontrivial torsion in higher Chow groups and the topological filtration of the associated generic variety and obtain new upper bounds for the annihilators of the torsion subgroups in the Chow groups of a la...

In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V|D|,δ), which parametrize universal families of irreducible, δ-nodal curves in a complete linear system |D|, on a smooth projective surface S of general type. We determine geometrical and numerical conditions on D and numerical conditions on δ ensuring that such number coincide...

It is well known that a Severi–Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi–Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra tec...

In this paper we construct some algebraic geometric error-correcting codes on surfaces whose Neron-Severi group has low rank. If the rank of the Neron-Severi group is 1, the intersection of this surface with an irreducible surface of lower degree will be an irreducible curve, and this makes possible the construction of codes with good parameters. Rank 1 surfaces are not easy to find, but we are...