Constraints on Sections Sample Clauses

Constraints on Sections. ‌ The sections σi can only intersect the multiplicity one components of the Kodaira fibers. To see this, first note that in the quartic in P[1,1,2], the sections are on equal footing, and only by mapping to a Weierstrass model, do we single out one of the sections as the origin of the elliptic curve, e.g. σ0 in (5.1.4). There is a symmetry that exchanges the two sections, and we can construct a Weierstrass model, with origin given by σ1: blow-down s = 0, after which there is a holomorphic coordinate shift that exchanges the sections σ0 ↔ σ1 ⇐⇒ y → y ± b0x2 . (5.1.14)
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