query: Can curves with different genuses be isomorohic?
positive_passages.docid: 148203
positive_passages.text: The genus of an algebraic curve is invariant under isomorphisms
negative_passages.docid: 127964
negative_passages.text: Confused about the possibility of different differentiable structures.
negative_passages.docid: 102274
negative_passages.text: Problem in Rick Miranda: finding genus of a projective curve
negative_passages.docid: 141911
negative_passages.text: Prove that these two fields are isomorphic.
negative_passages.docid: 81238
negative_passages.text: Is $O(2)$ really not isomorphic to $SO(2)\times \{-1,1\}$?
negative_passages.docid: 27581
negative_passages.text: Topologist's sine curve is connected
negative_passages.docid: 1283
negative_passages.text: Proper parametrization of a closed curve
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 95250
negative_passages.text: Proof a special extension on the isoperimetric theorem
negative_passages.docid: 47031
negative_passages.text: Isometric to Dual implies Hilbertable?
negative_passages.docid: 40490
negative_passages.text: Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
negative_passages.docid: 116588
negative_passages.text: All polynomial parametric curves in $k^2$ are contained in affine algebraic varieties
negative_passages.docid: 110472
negative_passages.text: Existence of a Pivot Point in Euclidean Geometry
negative_passages.docid: 118987
negative_passages.text: Birational map from elliptic curve keeps smoothness?
negative_passages.docid: 97637
negative_passages.text: Showing that isotropy groups are submanifolds
negative_passages.docid: 1531
negative_passages.text: Exercise from Geometry of algebraic curves by Arbarello, Cornalba, Griffiths, Harris
negative_passages.docid: 18718
negative_passages.text: How can curves be converted to meshes?