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New Faculty Publication: Prof. Hristo Iliev

April 02, 2021

Prof. Hristo Iliev with coauthors has just published a new article:

Choi, Y., Iliev, H., & Kim, S. (2021). Components of the Hilbert scheme of smooth projective curves using ruled surfaces. Manuscripta Mathematica, 164(3-4), 395-408. doi:10.1007/s00229-020-01188-0

Abstract: Let Id,g,r be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree d and genus g in Pr. We use families of curves on cones to show that under certain numerical assumptions for d, g and r, the scheme Id,g,r acquires generically smooth components whose general points correspond to curves that are double covers of irrational curves. In particular, in the case ρ(d, g, r) : = g- (r+ 1) (g- d+ r) ≥ 0 we construct explicitly a regular component that is different from the distinguished component of Id,g,r dominating the moduli space Mg. Our result implies also that if g≥ 57 then I4g3,g,g+12 has at least two generically smooth components parametrizing linearly normal curves. 

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