Varieties connected by chains of lines |
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| Authors: | Simone Marchesi Alex Massarenti |
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| Institution: | 1. IMECC-Unicamp, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária “Zeferino Vaz”, Distr. Bar?o Geraldo, CEP, 13083-859, Campinas, SP, Brasil
2. SISSA, via Bonomea 265, 34136, Trieste, Italy
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| Abstract: | In this paper we give for any integer $l\geqslant 2$ a numerical criterion ensuring the existence of a chain of length $l$ of lines through two general points of an irreducible variety $X \subset \mathbb P ^{N}$ , involving the degrees and the number of homogeneous polynomials defining $X$ . We show that our criterion is sharp. |
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