Genus four curve

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August undefined, 2024

WebWe construct a point in the Jacobian of a non-hyperelliptic genus four curve which is defined over a quadratic extension of the base field. We attempt to answer two questions: 1. Is this point torsion? 2. If not, does it generate the Mordell--Weil group of the Jacobian? We show that this point generates the Mordell--Weil group of the Jacobian of the universal … Webelliptic genus three curves endowed with a canonical pencil, in case (D) we get all hyperelliptic genus three curves endowed with a noncanonical pencil, and in case (E) every smooth genus four curve with an e ective even theta-characteristic so arises. Furthermore, for a general X!P1 the automorphism group of the bration has

The equations defining a curve of genus 4 - Semantic …

http://math.arizona.edu/%7Exuehang/thesis.pdf WebGENUS FOUR CURVE HANG XUE Abstract. In this paper, we construct a point on the Jacobian of a non-hyperelliptic genus four curve which is de ned over a quadratic extension of the base eld. We then show that this point generates the Mordell{Weil group of the Jacobian of the universal genus four curve. Contents 1. Statement of the theorem1 2. psychopathic the videos

Genus of a curve - Encyclopedia of Mathematics

Web• There is a genus four curve CK/Q whose rational points CK(Q) are in bijection with equivalence classes of irreducible trinomials f(x) = x5+ax+b so that K∼= Q[x]/(f(x)). • If Lis the smallest ﬁeld over which g(x) factors into a quadratic and a cubic in L[x], there is an elliptic curve E/Land a degree 2 map φ: CK → E deﬁned over L. Web153 3. Counting parameters suggests that Σ is a divisor: A curve lying in this locus has a degree 3 map to P 1 which is totally ramified above one point. So by the Riemann … http://math.stanford.edu/~vakil/files/twelvefinal.pdf psychopathic trance

The arithmetic and geometry of genus four curves

Determination of the 4-genus of a complete graph (with an …

WebFeb 23, 2024 · 2. The Wikipedia article Hyperelliptic curve states: In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the … WebSep 1, 2024 · In Section 2, we review some facts shown in [3] and [4] on superspecial curves of genus 4 and on their automorphisms, and explain an algorithm to determine … psychopathic theoryWebMar 31, 2024 · Curves of genus $ g = 1 $( elliptic curves, cf. Elliptic curve) are birationally isomorphic to smooth cubic curves in $ P ^ {2} $. The algebraic curves of genus $ g > 1 … hosts global washington dc

"WebThe primitive Teichmu¨ller curves in genus 2 are classiﬁed in [Mc2] and [Mc3]; in particular, it is shown (using [Mo]) that there is only one such curve lying outside S W ... Thus these four triangles furnish particular instances of Theorem 1.2. 2 Teichmu¨ller curves This section presents general results on holomorphic 1-forms, quadratic dif- " - Genus four curve

Genus four curve

Genus Definition & Meaning - Merriam-Webster

WebAug 23, 2024 · Download PDF Abstract: Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X can be obtained by intersecting the dual of the corresponding Cayley cubic … Web153 3. Counting parameters suggests that Σ is a divisor: A curve lying in this locus has a degree 3 map to P 1 which is totally ramified above one point. So by the Riemann-Hurwitz formula we get 2 g 2 6 3 2) + 2 + r where r is the number of other ramification points which we assume are all simple (to get maximal dimension), so r = 12 − 2 = 10.

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WebThe meaning of GENUS is a class, kind, or group marked by common characteristics or by one common characteristic; specifically : a category of biological classification ranking …

WebAug 23, 2024 · Download PDF Abstract: Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety … Webgroup of one genus four curve, up to isomorphism. The monodromy of the covering of this curve consists of one each of an order 2, 4, and 6 element (see ... We apply the same technique for the genus 5 curve whose automorphism group G is the GAP group (160,234). The monodromy here consists of one each of an

Webmodel of a genus four curve as above allows to reduce the initial mod-uli problem to a simple one in plane projective geometry; this last formulation leads to compute an explicit representation of a certain group on a vector space and its corresponding field of invariants. Let C be an irreducible, smooth, projective curve defined over the WebJul 29, 2024 · We apply Bridgeland stability conditions machinery to describe the geometry of some classical moduli spaces associated with canonical genus four curves in …

There are two related definitions of genus of any projective algebraic scheme X: the arithmetic genus and the geometric genus. When X is an algebraic curve with field of definition the complex numbers, and if X has no singular points, then these definitions agree and coincide with the topological definition applied to the Riemann surface of X (its manifold of complex points). For example, the definition of elliptic curve from algebraic geometry is connected non-singular projecti…

WebIn document Aspects of the Arithmetic of Uniquely Trigonal Genus Four Curves: Arithmetic Invariant Theory and Class Groups of Cubic Number Fields (Page 54-58) In this section, we apply the results of Section2.8to construct a genus 4 curve essential to the proof of Theorem3.3.9. We begin by providing some corollaries of Proposition2.8.4. hosts global texasWebIs it possible to construct a nonisotrivial family of genus four curves $X \rightarrow S$, with the following properties: (1) $S$ is a complete curve; (2) All the ... hosts go使用教程WebEquivalent curves on surfaces - Binbin XU 徐彬斌, Nankai (2024-12-20) We consider a closed oriented surface of genus at least 2. To describe curves on it, one natural idea is to choose once for all a collection of curves as a reference system and to hope that any other curve can be determined by its intersection numbers with reference curves. hosts globalhitssWebThe degree-genus formula g = 1 2 ( d − 1) ( d − 2) for plane curves tells you there is no smooth plane curve of genus 4. On the other hand, a nonsingular complete intersection of a quadric surface and a cubic surface in P 3 has genus 4, by a straightforward adjunction calculation. In fact adjunction shows that such a curve is canonically ... psychopathic vampiresWebWe construct some families of genus four curves over the function field of $\bP^1$ over a finite field and prove that half of the Jacobians in this family are generated by this point … hosts google adsWebThe general genus four curve is a smooth curve in P 1 P of type (3;3). The space of all (3;3)-curves on P1 P1 is a projective space Pof dimension 15. We consider the line … hosts go怎么用WebAbstract: Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a … psychopathic triad