Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links

Details Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links

2011-06-19

arxiv.org/abs/1106.3716v3

Mathematics

Algebraic Geometry

36 pages, to appear in Proc. London Math. Soc

Scientific paper

We characterise smooth curves in P^3 whose blow-up produces a threefold with anticanonical divisor big and nef. These are curves C of degree d and genus g lying on a smooth quartic, such that (i) $4d-30 \le g\le 14$ or $(g,d) = (19,12)$, (ii) there is no 5-secant line, 9-secant conic, nor 13-secant twisted cubic to C. This generalises the classical similar situation for the blow-up of points in P^2. We describe then Sarkisov links constructed from these blow-ups, and are able to prove the existence of Sarkisov links which were previously only known as numerical possibilities.

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