127:; and a function applied to a formal sum means the product (with multiplicities, poles counting as a negative multiplicity) of the values of the function at the points of the divisor. With this definition there must be the side-condition, that the divisors of
367:
Arbarello, E.; De
Concini, C.; Kac, V.G. (1989). "The infinite wedge representation and the reciprocity law for algebraic curves". In Ehrenpreis, Leon; Gunning, Robert C. (eds.).
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Theta functions, Bowdoin 1987. (Proceedings of the 35th Summer
Research Institute, Bowdoin Coll., Brunswick/ME July 6-24, 1987)
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291:, pp. 44â46, for this as a special case of a theory on mapping algebraic curves into commutative groups.
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405:. Graduate Texts in Mathematics. Vol. 117 (Translation of the French 2nd ed.). New York, etc.:
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is defined, in such a way that the statement given is equivalent to saying that the product over all
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339:. Wiley Classics Library. New York, NY: John Wiley & Sons Ltd. pp. 242â3.
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371:. Proceedings of Symposia in Pure Mathematics. Vol. 49. Providence, RI:
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To remove the condition of disjoint support, for each point
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Sur les fonctions algébriques à corps de constantes finis
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such that the function has neither a zero nor a pole at
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142:, this can be proved by manipulations with the
323:, a 1942 letter to Artin, explaining the 1940
135:have disjoint support (which can be removed).
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8:
335:Griffiths, Phillip; Harris, Joseph (1994).
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514:
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440:
432:
289:Groupes algébriques et corps de classes
877:Clifford's theorem on special divisors
107:where the notation has this meaning: (
123:of its zeroes and poles counted with
7:
201:terms, by considering (up to sign)
1035:Vector bundles on algebraic curves
969:Weber's theorem (Algebraic curves)
566:Hasse's theorem on elliptic curves
556:Counting points on elliptic curves
25:
403:Algebraic groups and class fields
337:Principles of Algebraic Geometry
185:of the local symbols is 1. When
657:Hurwitz's automorphisms theorem
193:both take the values 0 or â at
1065:Theorems in algebraic geometry
882:Gonality of an algebraic curve
793:Differential of the first kind
80:), i.e. rational functions on
1:
1025:BirkhoffâGrothendieck theorem
735:Nagata's conjecture on curves
606:SchoofâElkiesâAtkin algorithm
480:Five points determine a conic
373:American Mathematical Society
294:There is a generalisation of
226:. This is achieved by taking
596:Supersingular elliptic curve
803:Riemann's existence theorem
730:Hilbert's sixteenth problem
622:Elliptic curve cryptography
535:Fundamental pair of periods
1081:
933:Moduli of algebraic curves
230:to be the multiplicity of
59:algebraically closed field
250:. The definition is then
700:CayleyâBacharach theorem
627:Elliptic curve primality
119:, or in other words the
959:RiemannâHurwitz formula
923:GromovâWitten invariant
783:Compact Riemann surface
571:Mazur's torsion theorem
317:Oeuvres Scientifiques I
576:Modular elliptic curve
490:Rational normal curve
199:removable singularity
1030:Stable vector bundle
902:Weil reciprocity law
892:RiemannâRoch theorem
872:BrillâNoether theory
808:RiemannâRoch theorem
725:Genusâdegree formula
586:MordellâWeil theorem
561:Division polynomials
375:. pp. 171â190.
242:the multiplicity of
33:Weil reciprocity law
853:Structure of curves
745:Quartic plane curve
667:Hyperelliptic curve
647:De Franchis theorem
591:NagellâLutz theorem
359:for a proof in the
138:In the case of the
860:Divisors on curves
652:Faltings's theorem
601:Schoof's algorithm
581:Modularity theorem
399:Serre, Jean-Pierre
319:, p. 291 (in
64:. Given functions
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954:HasseâWitt matrix
897:Weierstrass point
844:Smooth completion
813:TeichmĂŒller space
715:Cubic plane curve
635:
634:
549:Arithmetic theory
530:Elliptic integral
525:Elliptic function
304:Abelian Varieties
300:abelian varieties
285:Jean-Pierre Serre
16:(Redirected from
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1060:Algebraic curves
887:Jacobian variety
857:
760:Riemann surfaces
750:Real plane curve
710:Cramer's paradox
690:BĂ©zout's theorem
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464:algebraic curves
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283:See for example
146:of polynomials.
115:of the function
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18:Weil reciprocity
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768:Belyi's theorem
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740:PlĂŒcker formula
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662:Hurwitz surface
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518:Analytic theory
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485:Projective line
472:Rational curves
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407:Springer-Verlag
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361:Riemann surface
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39:holding in the
35:is a result of
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964:Prym variety
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720:Fermat curve
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640:Higher genus
615:Applications
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839:Polar curve
29:mathematics
1054:Categories
834:Dual curve
462:Topics in
425:0703.14001
391:0699.22028
355:0836.14001
310:References
296:Serge Lang
121:formal sum
37:André Weil
947:Morphisms
695:Bitangent
144:resultant
111:) is the
401:(1988).
57:over an
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1007:Tacnode
992:Crunode
302:(Lang,
113:divisor
84:, then
987:Acnode
911:Moduli
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343:
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327:note
214:with
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997:Cusp
411:ISBN
377:ISBN
363:case
341:ISBN
218:and
189:and
131:and
68:and
421:Zbl
387:Zbl
351:Zbl
306:).
298:to
246:at
234:at
153:on
72:in
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