Topic
Base locus
About: Base locus is a research topic. Over the lifetime, 193 publications have been published within this topic receiving 2267 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, a generalization of the SHGH conjecture is proposed, where rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points.
Abstract: We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union of fat points imposes on the complete linear system of curves in of fixed degree , in terms of the occurrence of certain rational curves in the base locus of the linear subsystem defined by . As a first step towards a new theory, we show that rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points. Moreover, motivated by work of Di Gennaro, Ilardi and Valles and of Faenzi and Valles, we relate our results to the failure of a strong Lefschetz property, and we give a Lefschetz-like criterion for Terao’s conjecture on the freeness of line arrangements.
71 citations
TL;DR: In this paper, a pseudoeffective R-divisor for the blowup of P^3 at nine very general points which lies in the closed movable cone and has negative intersections with a set of curves whose union is Zariski dense was constructed.
Abstract: We exhibit a pseudoeffective R-divisor D_\lambda on the blow-up of P^3 at nine very general points which lies in the closed movable cone and has negative intersections with a set of curves whose union is Zariski dense. It follows that the diminished base locus B_-(D_\lambda) = \bigcup_{A ample}} B(D_\lambda+A) is not closed and that D_\lambda does not admit a Zariski decomposition in even a very weak sense. By a similar method, we construct an R-divisor on the family of blow-ups of P^2 at ten distinct points, which is nef on a very general fiber but fails to be nef over countably many prime divisors in the base.
62 citations
TL;DR: In this paper, the authors apply the theory of M-regularity developed by the authors [Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285-302] to the study of linear series given by multiples of ample line bundles.
Abstract: We apply the theory of M-regularity developed by the authors [Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285-302] to the study of linear series given by multiples of ample line bundles on abelian varieties. We define an invariant of a line bundle, called M-regularity index, which governs the higher order properties and (partly conjecturally) the defining equations of such embeddings. We prove a general result on the behavior of the defining equations and higher syzygies in embeddings given by multiples of ample bundles whose base locus has no fixed components, extending a conjecture of Lazarsfeld [proved in Syzygies of abelian varieties, J. Amer. Math. Soc. 13 (2000), 651-664]. This approach also unifies essentially all the previously known results in this area, and is based on Fourier-Mukai techniques rather than representations of theta groups.
59 citations
TL;DR: In this article, the authors classify all Gorenstein Fano threefold with at worst canonical singularities for which the anticanonical system has a nonempty base locus.
Abstract: We classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.
56 citations
Posted Content•
TL;DR: In this paper, it was shown that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF) with nonempty base locus.
Abstract: Here we show that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short) Furthermore, if b + (X) > 0 then it also has a Broken Lefschetz Pencil structure (BLP) with nonempty base locus This improves a theorem of Auroux, Donaldson and Katzarkov, and our proof is topological (ie uses 4-dimensional handlebody theory)
53 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 12 |
| 2020 | 10 |
| 2019 | 6 |
| 2018 | 15 |
| 2017 | 8 |
| 2016 | 12 |