Abel maps and limit linear series
نویسندگان
چکیده
منابع مشابه
Abel maps and limit linear series
Definition 2.1. Fix integers d and r. A limit (linear) series on X of degree d and rank r is a collection consisting of an invertible sheaf L on X of degree d on Y and degree 0 on Z, and vector subspaces Vi ⊆ Γ(X,L) of dimension r + 1, for each i = 0, . . . , d, such that φ(Vi) ⊆ Vi+1 and φi(Vi+1) ⊆ Vi for each i. Given a limit series (L, V0, . . . , Vd), we denote by V Y,0 i the subspace of Vi...
متن کامل. A G ] 1 5 Fe b 20 11 ABEL MAPS AND LIMIT LINEAR SERIES EDUARDO
We explore the relationship between limit linear series and fibers of Abel maps in the case of curves with two smooth components glued at a single node. To an r-dimensional limit linear series satisfying a certain exactness property (weaker than the refinedness property of Eisenbud and Harris) we associate a closed subscheme of the appropriate fiber of the Abel map. We then describe this closed...
متن کاملLimit linear series
Preface I hope that this book is simultaneously accessible on two different levels: first, most of the ideas should be comprehensible to the reader who has studied varieties but not schemes; and second, formal definitions and proofs are provided throughout for the reader who is familiar with schemes. On a third level, because it is not my intention to attempt to treat the moduli space of curves...
متن کاملAbel Maps and Presentation Schemes
We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding p...
متن کاملLimit Linear Series an Introduction
Our central objects of study are nonsingular curves, which were classically studied via linear series. Limit linear series are a generalization of linear series on nonsingular curves to (certain classes of) reducible curves. Their purpose is to examine how linear series degenerate on a family of smooth curves degenerating to a reducible curve. This degeneration technique can then be used to pro...
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: Rendiconti del Circolo Matematico di Palermo
سال: 2013
ISSN: 0009-725X,1973-4409
DOI: 10.1007/s12215-013-0111-0