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138:â„ 3 it is no longer the case that the genus determines the gonality. The gonality of the generic curve of genus
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are those with gonality 3, and this case gave rise to the name in general. Trigonal curves include the
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The
Geometry of Syzygies. A second course in commutative algebra and algebraic geometry
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195:, of M. Green and R. Lazarsfeld, predicts that the gonality of the algebraic curve
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17:
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122:
is algebraically closed, then the gonality is 1 precisely for curves of
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933:
290:
928:
289:, the notion (but not the terminology) originated in Section V of
81:, then the gonality is the minimum value taken by the degrees of
211:
of high degree. In many cases the gonality is two more than the
377:
266:
is zero, then the conjectured formula for the gonality is
362:
Code for constructing examples of special trigonal curves
355:
Geometric introduction to trigonal curves of genus five
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581:
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297:Amodeo used the term "gonalitĂ " as early as 1893.
134:(this includes all curves of genus 2). For genus
42:is defined as the lowest degree of a nonconstant
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243:), with respect to a given such embedding of
8:
126:0. The gonality is 2 for curves of genus 1 (
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165:, of genus three and given by an equation
235:large with respect to the genus. Writing
247:and the minimal free resolution for its
819:Clifford's theorem on special divisors
7:
219:is an exact formula in terms of the
977:Vector bundles on algebraic curves
911:Weber's theorem (Algebraic curves)
508:Hasse's theorem on elliptic curves
498:Counting points on elliptic curves
285:According to the 1900 ICM talk of
25:
599:Hurwitz's automorphisms theorem
318:. Vol. 229. New York, NY:
107:of the function field over its
824:Gonality of an algebraic curve
735:Differential of the first kind
111:generated by single functions
54:. In more algebraic terms, if
1:
967:BirkhoffâGrothendieck theorem
677:Nagata's conjecture on curves
548:SchoofâElkiesâAtkin algorithm
422:Five points determine a conic
316:Graduate Texts in Mathematics
538:Supersingular elliptic curve
295:Theory of Abelian Functions.
745:Riemann's existence theorem
672:Hilbert's sixteenth problem
564:Elliptic curve cryptography
477:Fundamental pair of periods
249:homogeneous coordinate ring
217:GreenâLazarsfeld conjecture
1023:
875:Moduli of algebraic curves
642:CayleyâBacharach theorem
569:Elliptic curve primality
251:, for the minimum index
901:RiemannâHurwitz formula
865:GromovâWitten invariant
725:Compact Riemann surface
513:Mazur's torsion theorem
518:Modular elliptic curve
364:on GitHub, written in
432:Rational normal curve
322:. pp. 171, 178.
199:can be calculated by
972:Stable vector bundle
844:Weil reciprocity law
834:RiemannâRoch theorem
814:BrillâNoether theory
750:RiemannâRoch theorem
667:Genusâdegree formula
528:MordellâWeil theorem
503:Division polynomials
221:graded Betti numbers
132:hyperelliptic curves
58:is defined over the
1007:Homological algebra
795:Structure of curves
687:Quartic plane curve
609:Hyperelliptic curve
589:De Franchis theorem
533:NagellâLutz theorem
201:homological algebra
193:gonality conjecture
802:Divisors on curves
594:Faltings's theorem
543:Schoof's algorithm
523:Modularity theorem
205:minimal resolution
989:
988:
985:
984:
896:HasseâWitt matrix
839:Weierstrass point
786:Smooth completion
755:TeichmĂŒller space
657:Cubic plane curve
577:
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491:Arithmetic theory
472:Elliptic integral
467:Elliptic function
16:(Redirected from
1014:
1002:Algebraic curves
829:Jacobian variety
799:
702:Riemann surfaces
692:Real plane curve
652:Cramer's paradox
632:BĂ©zout's theorem
457:
406:algebraic curves
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384:
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231:dimensions, for
209:invertible sheaf
188:is of degree 4.
83:field extensions
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944:Delta invariant
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809:AbelâJacobi map
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760:Torelli theorem
730:Dessin d'enfant
710:Belyi's theorem
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682:PlĂŒcker formula
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604:Hurwitz surface
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486:
460:Analytic theory
452:Elliptic curves
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427:Projective line
414:Rational curves
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320:Springer-Verlag
308:Eisenbud, David
306:
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287:Federico Amodeo
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159:Trigonal curves
128:elliptic curves
52:projective line
37:algebraic curve
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959:Vector bundles
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437:Riemann sphere
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213:Clifford index
203:means, from a
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144:floor function
105:
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75:function field
73:) denotes the
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18:Trigonal curve
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921:Singularities
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769:Constructions
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740:Klein quartic
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647:Conic section
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627:AF+BG theorem
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442:Twisted cubic
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329:0-387-22215-4
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227:embedding in
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223:for a degree
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163:Picard curves
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906:Prym variety
880:Stable curve
870:Hodge bundle
860:ELSV formula
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662:Fermat curve
619:Plane curves
582:Higher genus
557:Applications
482:Modular form
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44:rational map
39:
32:
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781:Polar curve
255:for which ÎČ
29:mathematics
996:Categories
776:Dual curve
404:Topics in
346:1066.14001
301:References
130:) and for
889:Morphisms
637:Bitangent
366:Macaulay2
109:subfields
310:(2005).
33:gonality
949:Tacnode
934:Crunode
338:2103875
291:Riemann
154:+ 3)/2.
142:is the
50:to the
929:Acnode
853:Moduli
344:
336:
326:
273:+ 1 â
215:. The
207:of an
184:where
35:of an
31:, the
124:genus
60:field
46:from
939:Cusp
324:ISBN
191:The
65:and
342:Zbl
293:'s
264:+ 1
146:of
118:If
77:of
27:In
998::
340:.
334:MR
332:.
314:.
281:).
260:,
172:=
115:.
95:)/
397:e
390:t
383:v
348:.
279:C
277:(
275:b
271:r
262:i
258:i
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245:C
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239:(
237:b
233:d
229:r
225:d
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186:Q
180:)
178:x
176:(
174:Q
170:y
152:g
150:(
140:g
136:g
120:K
113:f
103:)
101:f
99:(
97:K
93:C
91:(
89:K
79:C
71:C
69:(
67:K
63:K
56:C
48:C
40:C
20:)
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