Complex orientation formulas for $M$-curves of degree $4d+1$ with 4 nests

S.Yu. Orevkov

Displaying similar documents to “Complex orientation formulas for $M$ -curves of degree $4 d + 1$ with 4 nests”

Timelike $B_{2}$ -slant helices in Minkowski space $E_{1}^{4}$

Ahmad T. Ali, Rafael López (2010)

Archivum Mathematicum

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We consider a unit speed timelike curve $α$ in Minkowski 4-space $𝐄_{1}^{4}$ and denote the Frenet frame of $α$ by ${𝐓, 𝐍, 𝐁_{1}, 𝐁_{2}}$ . We say that $α$ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of $𝐄_{1}^{4}$ . In this work we study those helices where the function $〈 𝐁_{2}, U 〉$ is constant and we give different characterizations of such curves.

A group law on smooth real quartics having at least $3$ real branches

Johan Huisman (2002)

Journal de théorie des nombres de Bordeaux

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Let $C$ be a smooth real quartic curve in $ℙ^{2}$ . Suppose that $C$ has at least $3$ real branches $B_{1}, B_{2}, B_{3}$ . Let $B = B_{1} \times B_{2} \times B_{3}$ and let $O \in B$ . Let $τ_{O}$ be the map from $B$ into the neutral component Jac $(C) {(ℝ)}^{0}$ of the set of real points of the jacobian of $C$ , defined by letting $τ_{O} (P)$ be the divisor class of the divisor $\sum P_{i} - O_{i}$ . Then, $τ_{O}$ is a bijection. We show that this allows an explicit geometric description of the group law on Jac $(C) {(ℝ)}^{0}$ . It generalizes the classical geometric description of the group law on the neutral component of the set of real...

Labeled floor diagrams for plane curves

Sergey Fomin, Grigory Mikhalkin (2010)

Journal of the European Mathematical Society

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Floor diagrams are a class of weighted oriented graphs introduced by E. Brugallé and the second author. Tropical geometry arguments lead to combinatorial descriptions of (ordinary and relative) Gromov–Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In a number of cases, these descriptions can be used to obtain explicit (direct or recursive) formulas for the corresponding enumerative invariants. In particular, we use this approach to enumerate...

Codimension 1 subvarieties $ℳ_{g}$ and real gonality of real curves

Edoardo Ballico (2003)

Czechoslovak Mathematical Journal

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Let $ℳ_{g}$ be the moduli space of smooth complex projective curves of genus $g$ . Here we prove that the subset of $ℳ_{g}$ formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in $ℳ_{g}$ . As an application we show that if $X \in ℳ_{g}$ is defined over $ℝ$ , then there exists a low degree pencil $u X \to ℙ^{1}$ defined over $ℝ$ .

An iterative construction for ordinary and very special hyperelliptic curves

Francis J. Sullivan (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si costruiscono famiglie di curve iperellittiche col $p$ —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni $p$ -cicliche dei corpi con la caratteristica $p$ maggiore di zero.

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Jeremy Yirmeyahu Kaminski, Michael Fryers, Mina Teicher (2005)

Journal of the European Mathematical Society

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We study some geometric configurations related to projections of an irreducible algebraic curve embedded in $ℂ ℙ^{3}$ onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve $X$ embedded in $ℂ ℙ^{3}$ , of degree $d$ and genus $g$ , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining...

Optimal curves differing by a 5-isogeny

Dongho Byeon, Taekyung Kim (2014)

Acta Arithmetica

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For i = 0,1, let $E_{i}$ be the $X_{i} (N)$ -optimal curve of an isogeny class of elliptic curves defined over ℚ of conductor N. Stein and Watkins conjectured that E₀ and E₁ differ by a 5-isogeny if and only if E₀ = X₀(11) and E₁ = X₁(11). In this paper, we show that this conjecture is true if N is square-free and is not divisible by 5. On the other hand, Hadano conjectured that for an elliptic curve E defined over ℚ with a rational point P of order 5, the 5-isogenous curve E’ := E/⟨P⟩ has a rational...

Displaying similar documents to “Complex orientation formulas for M -curves of degree 4 d + 1 with 4 nests”

Timelike B 2 -slant helices in Minkowski space E 1 4

A group law on smooth real quartics having at least 3 real branches

Labeled floor diagrams for plane curves

Codimension 1 subvarieties ℳ g and real gonality of real curves

An iterative construction for ordinary and very special hyperelliptic curves

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Optimal curves differing by a 5-isogeny

Displaying similar documents to “Complex orientation formulas for $M$ -curves of degree $4 d + 1$ with 4 nests”

Timelike $B_{2}$ -slant helices in Minkowski space $E_{1}^{4}$

A group law on smooth real quartics having at least $3$ real branches

Codimension 1 subvarieties $ℳ_{g}$ and real gonality of real curves