Rational connectivity and sections of families over curves

Graber, T.M.; Harris, Joe; Mazur, Barry; Starr, Jason Michael

doi:10.1016/j.ansens.2005.07.003

Cited by 27 publications

(31 citation statements)

References 12 publications

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“…The same technique "completes" the strategy from Graber et al (2005) proving that the family of witness curves for dimension d depends on the integer d. …”

mentioning

confidence: 97%

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A pencil of Enriques surfaces of index one with no section

Starr

2009

ANT

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“…The same technique "completes" the strategy from Graber et al (2005) proving that the family of witness curves for dimension d depends on the integer d. …”

mentioning

confidence: 97%

“…This paper uses monodromy and deformation-and-specialization to answer some questions related to [Graber et al 2005]. …”

Section: Introductionmentioning

confidence: 99%

A pencil of Enriques surfaces of index one with no section

Starr

2009

ANT

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“…(Sketch only, see also similar arguments in [GHMS05].) Curve means irreducible and reduced closed subscheme of dimension 1.…”

Section: Main Theoremmentioning

confidence: 99%

Families of rationally simply connected varieties over surfaces and torsors for semisimple groups

Jong

Starr

2011

Publ.math.IHES

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Abstract. Under suitable hypotheses, we prove that a form of a projective homogeneous variety G/P defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an algebrogeometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we complete the proof of Serre's Conjecture II in Galois cohomology for function fields over an algebraically closed field.

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“…However, something weaker holds: there exists a subvariety Z ⊂ X for which the restriction f | Z : Z → Y is dominant with rationally connected general fiber. In [GHMS02] such Z is called a pseudosection of f . Recall that a point is rationally connected, so a section of f is a pseudosection.…”

Section: A Converse Of Theorem 210mentioning

confidence: 99%