D. Eisenbud, J. Koh, M. Stillman, Determinantal equations for curves of high degree, Amer. J. Math. 110 (1988), 513-539. Home/Search Document Not in Database Summary Related Articles Check |
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Abeliants And Their Application To An Elementary Construction Of .. - Anderson (2002) (Correct)
....emerging from the second stage of our construction seems well suited to machine computation and (ironically) is probably of greater value from a practical point of view than the explicit defining equation yoga emerging from the first stage. It is appropriate at this point to mention that the paper [Eisenbud Koh Stillman 1988] was a very important influence: we learned from it the folkloric concept of representation of divisor classes by rank one matrices. We believe, however, that our idea to exploit the theory of [Mumford 1970] in order to get a simple matrix representation of divisor class addition is new. We ignore ....
....The map D ## UDVD sends distinct divisor classes into distinct k equivalence classes (4.2.8) The image of the map D ## UDVD meets every k equivalence class of G forms (4.2.6) # 4.2.10. Remark. The dictionary set up by Proposition 4.2. 9 is a chapter of algebrogeometrical folklore; see [Eisenbud Koh Stillman 1988, Prop. 1.1] The EisenbudKoh Stillman paper greatly inspired us. Our presentation of the dictionary is a simplified version of the presentation in [Anderson 1997] 4.3. Matrix representation of divisor class addition and subtraction. We translate addition and subtraction of divisor classes into ....
Eisenbud, D., Koh, J., Stillman, M.: Determinantal equations for curves of high degree. Amer. J. Math. 110(1988)513-539.
Equations of (1,d)-polarized Abelian Surfaces - Gross, Popescu (1997) (Correct)
....hand Sec 3 (E) is an irreducible fivefold, hence an irreducible hypersurface in P 6 , whose equation being also H 7 invariant must have degree divisible by 7. It follows necessarily that Sec 3 (E) fF = 0g. In the remainder of this section, we relate the above approach to the main result of [EKS], which in turn enables us to give a more geometrical explanation for the above 19 matrices. Let X P n = P(V ) be a non degenerate, reduced, irreducible scheme and assume we can write L = OX (1) L 1 Omega L 2 for suitable line bundles L 1 and L 2 on X. Suppose also that V i ae H 0 ....
.... and linear series as above through the following correspondence: L 1 = im(M : O Phiv 1 X O Phiv 2 X (1) L 2 = im(M t : O Phiv 2 X O Phiv 1 X (1) V 1 = im(M : H 0 (O Phiv 1 X ) H 0 (L 1 ) V 2 = im(M t : H 0 (O Phiv 2 X ) H 0 (L 2 ) The main result of [EKS] asserts that if X is a reduced, irreducible curve of genus g and L i , i = 1; 2, are line bundles on X of degrees at least 2g 1, nonisomorphic in case both have degree 2g 1 and g 0, then the 2 Theta 2 minors of the matrix defined above generate the homogeneous ideal I X of X embedded via L ....
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Eisenbud, D., Koh, J., Stillman, M., "Determinantal equations for curves of high degree", Amer. J. of Math., 110, (1988) 513--539.
Abeliants and their application to an elementary.. - School Of Mathematics (Correct)
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D. Eisenbud, J. Koh, M. Stillman, Determinantal equations for curves of high degree, Amer. J. Math. 110 (1988), 513-539.
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