Third order nondegenerate homotopies of space curves
نویسندگان
چکیده
منابع مشابه
Topology of the Space of Nondegenerate Closed Curves
A curve on a sphere, aane or projective space is called nondegenerate if its osculating frame is nondegenerate at every point. We calculate the number of connected components in the space of all closed nondegenerate curves immersed into S n ; R n or P n. In the cases of S n or R n it is equal to 4 for odd n > 3 and 6 for even n > 4 (for S 2 the answer is also 6). For projective space P n the nu...
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Let Mg be the moduli space of curves of genus g ≥ 2, and let M g be the locus of curves which are birational to a curve defined by a nondegenerate bivariate Laurent polynomial. We show that dimM g = min(2g+1, 3g−3) except for g = 7 where dimM 7 = 16. In particular, a generic curve of genus g is nondegenerate if and only if g ≤ 4. Subject classification: 14M25, 14H10 Let k be a field with algebr...
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In this paper we present a p-adic algorithm to compute the zeta function of a nondegenerate curve over a finite field using Monsky-Washnitzer cohomology. The paper vastly generalizes previous work since in practice all known cases, e.g. hyperelliptic, superelliptic and Cab curves, can be transformed to fit the nondegenerate case. For curves with a fixed Newton polytope, the property of being no...
متن کاملON THE NUMBER OF CONNECTED COMPONENTS IN THE SPACE OF CLOSED NONDEGENERATE CURVES ON Sn
The main definition. A parametrized curve : I ! R n is called nonde-generate if for any t 2 I the vectors 0 (t); : : : ; (n) (t) are linearly independent. Analogously : I ! S n is called nondegenerate if for any t 2 I the covariant derivatives 0 (t); : : : ; (n) (t) span the tangent hyperplane to S n at the point (t) (compare with the notion of n-freedom in G]).
متن کاملOn the Number of Connected Components in the Space of Closed Nondegenerate Curves on S
The main definition. A parametrized curve γ : I → R is called nondegenerate if for any t ∈ I the vectors γ′(t), . . . , γ(t) are linearly independent. Analogously γ : I → S is called nondegenerate if for any t ∈ I the covariant derivatives γ′(t), . . . , γ(t) span the tangent hyperplane to S at the point γ(t) ( compare with the notion of n-freedom in [G]). Fixing an orientation in R or S we cal...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1971
ISSN: 0022-040X
DOI: 10.4310/jdg/1214430012