Pencils of Plane Curves and Characteristic Varieties

نویسنده

  • ALEXANDRU DIMCA
چکیده

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M. Falk and S. Yuzvinsky [10] in the case of line arrangements. In this case, this geometric point of view was already hinted to by A. Libgober and S. Yuzvinsky, see [15], Section 7.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Real Congruence of Complex Matrix Pencils and Complex Projections of Real Veronese Varieties

Quadratically parametrized maps from a real projective space to a complex projective space are constructed as projections of the Veronese embedding. A classification theorem relates equivalence classes of projections to real congruence classes of complex symmetric matrix pencils. The images of some low-dimensional cases include certain quartic curves in the Riemann sphere, models of the real pr...

متن کامل

Multinets, Resonance Varieties, and Pencils of Plane Curves

We show that a line arrangement in the complex projective plane supports a nontrivial resonance variety if and only if it is the underlying arrangement of a “multinet,” a multi-arrangement with a partition into three or more equinumerous classes which have equal multiplicities at each inter-class intersection point, and satisfy a connectivity condition. We also prove that this combinatorial str...

متن کامل

A New Bound on the Number of Special Fibers in a Pencil of Curves

In paper [9] it was proved that any pencil of plane curves of degree d > 1 with irreducible generic fiber can have at most five completely reducible fibers although no examples with five such fibers were ever found. Recently Janis Stipins has proved in [10] that if a pencil has the base of d points then it cannot have five completely reducible fibers. In this paper we generalize Stipins’ result...

متن کامل

Resonance varieties over fields of positive characteristic

Let A be a hyperplane arrangement, and k a field of arbitrary characteristic. We show that the projective degree-one resonance variety R(A, k) of A over k is ruled by lines, and identify the underlying algebraic line complex L(A, k) in the Grassmannian G(2, kn), n = |A|. L(A, k) is a union of linear line complexes corresponding to the neighborly partitions of subarrangements of A. Each linear l...

متن کامل

Characteristic Varieties and Constructible Sheaves

We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed as a continuation of D. Arapura’s paper [1], yields new geometric insight into the translated components relating them to the multiplicities of curves in the ...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006