Global divisors on an algebraic curve
نویسندگان
چکیده
If L is a field and R a subring of L, we define the lattice Val(L,R) as the lattice generated by symbols VR(s) for s in L with the relations 1. 1 = VR(r) if r is in R 2. VR(s) ∧ VR(t) 6 VR(s+ t) 3. VR(s) ∧ VR(t) 6 VR(st) 4. 1 = VR(s) ∨ VR(s) if s 6= 0 Contrary to the Zariski lattice, we cannot in general simplify an expression VR(s1) ∧ . . . ∧ V (sn) to a single basic open VR(s). Two exceptions can be noticed. We always have VR(r 1 )∧ VR(r 2 ) = VR((r1r2) −1) if r1, r2 non zero elements in R. For any non zero s in L we have VR(s) ∧ VR(s) = VR(s+ s−1)
منابع مشابه
Geometry of Algebraic Curves
The canonical divisor on a smooth plane curve 30 6.2. More general divisors on smooth plane curves 31 6.3. The canonical divisor on a nodal plane curve 32 6.4. More general divisors on nodal plane curves 33
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