Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Measures of irrationality for hypersurfaces of large degree

  • Part of
  • Francesco Bastianelli, Pietro De Poi, Lawrence Ein, Robert Lazarsfeld, Brooke Ullery
  • Journal:
    Compositio Mathematica / Volume 153 / Issue 11 / November 2017
    Published online by Cambridge University Press:
    04 September 2017, pp. 2368-2393
    Print publication:
    November 2017
    • Article
      • You have access
    • PDF
    • HTML
    • Export citation

  • We study various measures of irrationality for hypersurfaces of large degree in projective space and other varieties. These include the least degree of a rational covering of projective space, and the minimal gonality of a covering family of curves. The theme is that positivity properties of canonical bundles lead to lower bounds on these invariants. In particular, we prove that if $X\subseteq \mathbf{P}^{n+1}$ is a very general smooth hypersurface of dimension $n$ and degree $d\geqslant 2n+1$, then any dominant rational mapping $f:X{\dashrightarrow}\mathbf{P}^{n}$ must have degree at least $d-1$. We also propose a number of open problems, and we show how our methods lead to simple new proofs of results of Ran and Beheshti–Eisenbud concerning varieties of multi-secant lines.

  • Diophantine properties of real numbers generated by finite automata

  • Boris Adamczewski, Julien Cassaigne
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 6 / November 2006
    Published online by Cambridge University Press:
    24 November 2006, pp. 1351-1372
    Print publication:
    November 2006
    • Article
      • You have access
    • PDF
    • Export citation

  • We study some Diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the $b$-adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit.