Gaps for geometric genera

Authors :: Flaminio Flamini
Ciro Ciliberto
Mikhail Zaidenberg
Dipartimento di Matematica (Roma Tre)
Università degli Studi di Roma Tor Vergata [Roma]
Dipartimento di Matematica, Universitá degli Studi di Roma 'Tor Vergata'
Università degli Studi di Roma Tor Vergata [Roma]-Università degli Studi di Roma Tor Vergata [Roma]
Institut Fourier (IF )
Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Institut Fourier (IF)
Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
Source :: Archiv der Mathematik, Archiv der Mathematik, Springer Verlag, 2016, 106 (6), pp.531-541. ⟨10.1007/s00013-016-0908-0⟩
Publication Year :: 2016
Publisher :: Springer Science and Business Media LLC, 2016.
Abstract: We investigate the possible values for geometric genera of subvarieties in a smooth projective variety. Values which are not attained are called gaps. For curves on a very general surface in $\mathbb{P}^3$, the initial gap interval was found by Xu (see [7] in References), and the next one in our previous paper (see [4] in References), where also the finiteness of the set of gaps was established and an asymptotic upper bound of this set was found. In the present paper we extend some of these results to smooth projective varieties of arbitrary dimension using a different approach.<br />9 pages, submitted preprint

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