Seminar Algebra and Geometry: Jakub Witaszek (Imperial College London)

Effective bounds on positive characteristic singular surfaces

The famous Fujita conjecture says that K_X + (d+2)A is very ample, where X is a smooth projective variety of dimension d, and A is an ample divisor. Despite its simple statement, the conjecture is only known for d < 3 in characteristic zero. In positive characteristic, the conjecture hasn't been even proved for surfaces, but thanks to the recent progress due to Di Cerbo and Fanelli, we know that when X is a projective smooth surface there exist constants a, b ∈ ℕ such that aK_X + bA is very ample. In this talk, we will discuss similar bounds in the case when X is singular.

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