A Torelli-like Theorem for Smooth Plane Curves
نویسنده
چکیده
The Information-Theoretic Schottky Problem treats the period matrix of a compact Riemann Surface as a compressible signal. In this case, the period matrix of a smooth plane curve is characterized by only 4 of its columns, a significant compression.
منابع مشابه
Moduli of Surfaces with an Anti-Canonical Cycle
We prove a global Torelli theorem for pairs (Y,D) where Y is a smooth projective rational surface and D ∈ |−KY | is a cycle of rational curves, as conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.
متن کاملTORELLI THEOREM FOR MODULI SPACES OF SL(r,C)–CONNECTIONS ON A COMPACT RIEMANN SURFACE
Let X be any compact connected Riemann surface of genus g, with g ≥ 3. For any r ≥ 2, let MX denote the moduli space of holomorphic SL(r, C)–connections over X . It is known that the biholomorphism class of the complex variety MX is independent of the complex structure of X . If g = 3, then we assume that r ≥ 3. We prove that the isomorphism class of the variety MX determines the Riemann surfac...
متن کاملFiniteness and Torelli Spaces
Torelli space Tg (g ≥ 2) is the quotient of Teichmüller space by the Torelli group Tg. It is the moduli space of compact, smooth genus g curves C together with a symplectic basis of H1(C;Z) and is a model of the classifying space of Tg. Mess, in his thesis [12], proved that T2 has the homotopy type of a bouquet of a countable number of circles. Johnson and Millson (cf. [12]) pointed out that a ...
متن کاملCubic Threefolds and Abelian Varieties of Dimension Five
Cubic threefolds have been studied in algebraic geometry since classical times. In [5], Clemens and Griffiths proved that the intermediate Jacobian JX of a smooth cubic threefold is not isomorphic as a principally polarized abelian variety to a product of Jacobians of curves, which implies the irrationality of X. They also established the Torelli theorem for cubic threefolds: the principally po...
متن کاملTwo Characteristic Numbers for Smooth Plane Curves of Any Degree
We use a sequence of blow-ups over the projective space parametrizing plane curves of degree d to obtain some enumerative results concerning smooth plane curves of arbitrary degree. For d = 4 , this gives a first modem verification of results of H. G. Zeuthen. O. INTRODUCTION The kth 'characteristic number' of the d(dt3) -dimensional family of smooth plane curves of degree d, denoted Nd(k) in t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1212.4912 شماره
صفحات -
تاریخ انتشار 2012