Download A scrapbook of complex curve theory by C. Herbert Clemens PDF

By C. Herbert Clemens

ISBN-10: 0306405369

ISBN-13: 9780306405365

This high-quality ebook through Herb Clemens quick turned a favourite of many complicated algebraic geometers whilst it used to be first released in 1980. it's been well liked by newbies and specialists ever due to the fact that. it's written as a publication of "impressions" of a trip during the concept of complicated algebraic curves. Many themes of compelling good looks ensue alongside the way in which. A cursory look on the matters visited unearths an it appears eclectic choice, from conics and cubics to theta capabilities, Jacobians, and questions of moduli. through the top of the booklet, the subject matter of theta features turns into transparent, culminating within the Schottky challenge. The author's cause used to be to encourage additional research and to stimulate mathematical job. The attentive reader will study a lot approximately advanced algebraic curves and the instruments used to review them. The publication might be specifically beneficial to a person getting ready a path concerning advanced curves or a person attracted to supplementing his/her examining

Show description

Read Online or Download A scrapbook of complex curve theory PDF

Similar algebraic geometry books

The Geometry of Moduli Spaces of Sheaves

Now again in print, this extremely popular e-book has been up-to-date to mirror fresh advances within the thought of semistable coherent sheaves and their moduli areas, which come with moduli areas in optimistic attribute, moduli areas of imperative bundles and of complexes, Hilbert schemes of issues on surfaces, derived different types of coherent sheaves, and moduli areas of sheaves on Calabi-Yau threefolds.

Spaces of Homotopy Self-Equivalences: A Survey

This survey covers teams of homotopy self-equivalence sessions of topological areas, and the homotopy form of areas of homotopy self-equivalences. For manifolds, the whole crew of equivalences and the mapping classification workforce are in comparison, as are the corresponding areas. incorporated are tools of calculation, a number of calculations, finite iteration effects, Whitehead torsion and different components.

Galois Theory of Difference Equations

This publication lays the algebraic foundations of a Galois concept of linear distinction equations and exhibits its courting to the analytic challenge of discovering meromorphic features asymptotic to formal suggestions of distinction equations. Classically, this latter query was once attacked through Birkhoff and Tritzinsky and the current paintings corrects and tremendously generalizes their contributions.

Additional info for A scrapbook of complex curve theory

Example text

Since for every n there are maps M ( B / p n B , kn, N;r) -~ M ( B / p " B , k , . N ; 1 ) , taking the inverse limit gives a map M(B, X(i,k), N; r) , M(B, X(,,k), N; 1). It is not clear that this map is an inclusion, because the maps modulo p'~ are not injective. 1 Let the spaces M(B,X(i,~),N;r) and the maps M(B,x(~,k),N;r) , M(B, X(i,k), N; 1) be defined as above. Are the maps c~ inclusions? In other words, can we think of overconvergent forms of weight (i,k) (as defined above) as a certain kind of p-adic modular forms of weight (i, k) ?

P We claim there is an injection D ~ V ( B , N). To see this, let ~" E B be a uniformizer, and let f = ~ f~ E D, where fi E M(K, Np ~',i). T h e n we have f(q) E B[[q]], and, for some n, 7r'~f E ~ M(B,i, Np~), hence ~r"f E V. Then, since (Tr'~f)(q) = 7r'~f(q), f(q) B((q))/V. 1 above), it follows t h a t there exists ] E V such t h a t ](q) = f(q). Hence we m a y define ot D f ,--+ , , V ] . 12) Note t h a t the injectivity follows at once from the equality of the q-expanslons, since B is flat over Zp.

This allows us to define "slope a eigenspaces" for U which generalize (the integral weight case of) Hida's space of "ordinary p-adic modular forms". This will also show that there are few eigenforms for U outside its kernel, in the precise sense that if we fix the weight of f and the valuation of )~, one gets only a finite dimensional space of overconvergent forms of the given weight with eigenvalues of the given valuation. In contrast, it is clear that, even in the overconvergent case, ker(U) is quite large (in fact, infinite-dimensional), because of the Frobenius endomorphism: given any f E M(B,k,N;r), we have f - F r o b V f C ker(U).

Download PDF sample

A scrapbook of complex curve theory by C. Herbert Clemens


by David
4.0

Rated 4.28 of 5 – based on 30 votes