Irrationality and monodromy for cubic threefolds
نویسندگان
چکیده
منابع مشابه
Weight-monodromy Conjecture for Certain Threefolds in Mixed Characteristic
The weight-monodromy conjecture claims the coincidence of the shifted weight filtration and the monodromy filtration on étale cohomology of a proper smooth variety over a complete discrete valuation field. Although it was already proved in some cases, the case of dimension ≥ 3 in mixed characteristic is still unproved up to now. The aim of this paper is to prove the weight-monodromy conjecture ...
متن کاملCorrado Segre and Nodal Cubic Threefolds
We discuss the work of Corrado Segre on nodal cubic hypersurfaces with emphasis on the cases of 6-nodal and 10-nodal cubics. In particular we discuss the Fano surface of lines and conic bundle structures on such threefolds. We review some of the modern research in algebraic geometry related to Segre’s work.
متن کاملArithmetic Torelli Maps for Cubic Surfaces and Threefolds
It has long been known that to a complex cubic surface or threefold one can canonically associate a principally polarized abelian variety. We give a construction which works for cubics over an arithmetic base, and in particular identifies the moduli space of cubic surfaces with an open substack of a certain moduli space of abelian varieties. This answers, away from the prime 2, an old question ...
متن کاملPrym varieties and the Schottky problem for cubic threefolds
A theorem of Mumford’s states that for a smooth cubic threefold X, the intermediate Jacobian JX is a principally polarized abelian variety of dimension 5 whose theta divisor has a unique singular point, which has multiplicity three. This talk describes joint work with R. Friedman, in which we prove a converse: if A is a principally polarized abelian variety of dimension 5 whose theta divisor ha...
متن کاملCurves of Small Degree on Cubic Threefolds
In this article we consider the spaces H(X) parametrizing smooth curves of degree d and genus g on a smooth cubic threefold X ⊂ . For 1 ≤ d ≤ 5, we show that each variety H(X) is irreducible of dimension 2d.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali della Scuola normale superiore di Pisa. Classe di scienze
سال: 2022
ISSN: ['0391-173X', '2036-2145']
DOI: https://doi.org/10.2422/2036-2145.202005_006