Algebraic Geometry Sundance 1986: Proceedings of a - download pdf or read online

By Audun Holme, Robert Speiser

ISBN-10: 3540192360

ISBN-13: 9783540192367

ISBN-10: 3540391576

ISBN-13: 9783540391579

This quantity offers chosen papers because of the assembly at Sundance on enumerative algebraic geometry. The papers are unique examine articles and focus on the underlying geometry of the subject.

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Additional resources for Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986

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Ii) C is c o n t a i n e d in s o m e h v p e r s u r f a c e of degree e not containing S, a n d in a neighborhood of s o m e point of ~(C0), C is cut out s c h e m e theoretically b y h v p e r s u r f a c e s of degree e. iii) e_> a a n d ( e - a ) c 2b l~emark: If t h e r e is a h y p e r s u r f a c e of degree e containing C b u t not containing ~0(C0), t h e n condition ii) is satisfied. 1 bis: Condition i) trivially implies condition ii). Suppose t h a t condition ii) is satisfied. It follows t h a t t h e linear series [eH-C~ does not h a v e C0 as a base c o m p o n e n t .

Then the dimension of S(d, B,C, and A; a s s u m e t h a t 0<_ 8_< ~ ( d - l ) ( d 8) as a vector space over • is: i). dimS(d, O) = i ii). dimS(d, i) = 2 iii). dimS(d, 2) = 3 iv). dimS(d, 8) = 4 for 3 <_ 8 <_ ~(d-1)(d-2) - 2, v). e. g = 1), vi). e. g = 0). Proof: W(d, 0) is IPN with a set of codimension 2 r e m o v e d so clearly d i m S ( d , 0) = i. 4) we h a v e span(A, B, C, A} = span{CU, TN, TR, A} = span{CU, TN, TR, NL}. 35 For 8 = 1, TN = 0 so d i m S ( d , i ) s 2. For 8-- 2, T R - - 0 so d i m S ( d , 2)_< 3.

5). 6) Theorem: Let S(d, 8) c Pic(W(d, 8)) ® Q be the subspace spanned b y A, 2). Then the dimension of S(d, B,C, and A; a s s u m e t h a t 0<_ 8_< ~ ( d - l ) ( d 8) as a vector space over • is: i). dimS(d, O) = i ii). dimS(d, i) = 2 iii). dimS(d, 2) = 3 iv). dimS(d, 8) = 4 for 3 <_ 8 <_ ~(d-1)(d-2) - 2, v). e. g = 1), vi). e. g = 0). Proof: W(d, 0) is IPN with a set of codimension 2 r e m o v e d so clearly d i m S ( d , 0) = i. 4) we h a v e span(A, B, C, A} = span{CU, TN, TR, A} = span{CU, TN, TR, NL}.

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Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986 by Audun Holme, Robert Speiser


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