Hodge Structures and Differential Operators
نویسندگان
چکیده
These are extended notes of my talk at the IMPANGA seminar in Warsaw on October 11, 2019. The goal was to give a non-technical and arithmetically motivated introduction definition limiting mixed Hodge structure by Schmid Deligne. We state several assertions terms natural classical theory ordinary differential operators prove them using elementary arguments. References geometric context only made few remarks examples, which can be easily skipped reader not familiar with algebro-geometric techniques.
منابع مشابه
Exterior Differential Systems and Variations of Hodge Structures
Aside from the classical case of abelian varieties and K3 surfaces, the period matrices of algebraic varieties varying in a family are subject to differential constraints; i.e., they satisfy a PDE system. We will explain two algebro-geometric consequences of the integrability conditions of this PDE system. We will also discuss a related, potentially quite interesting, conjecture. Outline I. Ext...
متن کاملDiscrete Hodge operators
Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduce...
متن کاملHodge Groups of Hodge Structures with Hodge Numbers
This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...
متن کاملHodge Structures on Posets
Let P be a poset with unique minimal and maximal elements 0̂ and 1̂. For each r, let Cr(P ) be the vector space spanned by r-chains from 0̂ to 1̂ in P . We define the notion of a Hodge structure on P which consists of a local action of Sr+1 on Cr, for each r, such that the boundary map ∂r : Cr → Cr−1 intertwines the actions of Sr+1 and Sr according to a certain condition. We show that if P has a Ho...
متن کاملNonabelian mixed Hodge structures
We propose a definition of “nonabelian mixed Hodge structure” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V , the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure denoted H = Hom(XM , V ). We describe the basic definitions and then give some conjectures saying what is su...
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: Springer proceedings in mathematics & statistics
سال: 2021
ISSN: ['2194-1009', '2194-1017']
DOI: https://doi.org/10.1007/978-3-030-84304-5_5