New PDF release: Advances in Moduli Theory

By Yuji Shimizu and Kenji Ueno

ISBN-10: 0821821563

ISBN-13: 9780821821565

Shimizu and Ueno (no credentials indexed) reflect on numerous features of the moduli conception from a posh analytic standpoint. they supply a quick creation to the Kodaira-Spencer deformation concept, Torelli's theorem, Hodge concept, and non-abelian conformal thought as formulated through Tsuchiya, Ueno, and Yamada. in addition they speak about the relation of non-abelian conformal box idea to the moduli of vector bundles on a closed Riemann floor, and exhibit tips to build the moduli thought of polarized abelian forms.

Show description

Read or Download Advances in Moduli Theory PDF

Best algebraic geometry books

Complex functions: An algebraic and geometric viewpoint - download pdf or read online

Elliptic features and Riemann surfaces performed a major position in nineteenth-century arithmetic. today there's a nice revival of curiosity in those subject matters not just for his or her personal sake but in addition due to their purposes to such a lot of parts of mathematical learn from team concept and quantity conception to topology and differential equations.

Download e-book for kindle: Concise course in algebraic topology by J. P. May

Algebraic topology is a easy a part of sleek arithmetic, and a few wisdom of this zone is integral for any complicated paintings on the subject of geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This ebook presents an in depth remedy of algebraic topology either for lecturers of the topic and for complex graduate scholars in arithmetic both focusing on this sector or carrying on with directly to different fields.

Additional info for Advances in Moduli Theory

Sample text

Then E is said to be (semi)stable, if for all subsheaves F ⊂ E with 0 < rk(F ) < rk(E) one has μ(F )(≤)μ(E). Note that this is equivalent to our stability condition p(F )(≤)p(E). 10 — Examples of stable or semistable bundles are easily available: any line bundle is stable. Furthermore, if 0 → L0 → F → L1 → 0 is a non-trivial extension with line bundles L0 and L1 of degree 0 and 1, respectively, then F is stable: since the degree is additive, we have deg(F ) = 1 and μ(F ) = 1/2. Let M ⊂ F be an arbitrary subsheaf.

I − 1 and let Fj be the preimage of Ej+1 /Ei for j = i, . . , − 1. The induction hypothesis applied to F gives 24 = Preliminaries and Ej /Ej−1 ∼ = j=1 Since E1 ∼ = Ei /Ei−1 , we are done. Ej /Ej−1 . 3 — Two semistable sheaves E1 and E2 with the same reduced Hilbert polynomial are called S-equivalent if gr(E1 ) ∼ = gr(E2 ). The importance of this definition will become clear in Section 4. Roughly, the moduli space of semistable sheaves parametrizes only S-equivalence classes of semistable sheaves.

If g : T → S is an Sscheme we will use the notation XT for the fibre product T ×S X, and gX : XT → X and fT : XT → T for the natural projections. For s ∈ S the fibre f −1 (s) = Spec(k(s)) ×S X ∗ is denoted Xs . Similarly, if F is a coherent OX -module, we write FT := gX F and Fs = F |Xs . Often, we will think of F as a collection of sheaves Fs parametrized by s ∈ S. 1 — A flat family of coherent sheaves on the fibres of f is a coherent OX -module F which is flat over S. 1 Flat Families and Determinants 35 Recall that this means that for each point x ∈ X the stalk Fx is flat over the local ring OS,f (x) .

Download PDF sample

Advances in Moduli Theory by Yuji Shimizu and Kenji Ueno

by Ronald

Rated 4.13 of 5 – based on 31 votes