We are concerned with limits of Weierstrass points under degeneration of smooth curves to stable curves of non compact type, union of two irreducible smooth components meeting transversely at points. The case having already been treated by Eisenbud and Harris in [8], we analyze the situation for .
We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general position. As an application, we obtain a classification of special linear systems on ℙ¹×ℙ¹ with multiplicities not exceeding 3.
2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply...
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a 𝕂-analytic curve is a finite-dimensional vector space. We also show that the action of local diffeomorphisms preserving the quasi-homogeneous curve on this vector space is determined by the infinitesimal action of...
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...
Let be a field of characteristic , a proper, smooth, geometrically connected curve over , and 0 and two -rational points on . We show that any representation of the local Galois group at extends to a representation of the fundamental group of which is tamely ramified at 0, provided either that is separately closed or that is . In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental group...