By Piotr Pragacz
The articles during this quantity are committed to:
- moduli of coherent sheaves;
- crucial bundles and sheaves and their moduli;
- new insights into Geometric Invariant Theory;
- stacks of shtukas and their compactifications;
- algebraic cycles vs. commutative algebra;
- Thom polynomials of singularities;
- 0 schemes of sections of vector bundles.
The major objective is to offer "friendly" introductions to the above issues via a chain of accomplished texts ranging from a really basic point and finishing with a dialogue of present study. In those texts, the reader will locate classical effects and techniques in addition to new ones. The e-book is addressed to researchers and graduate scholars in algebraic geometry, algebraic topology and singularity concept. lots of the fabric awarded within the quantity has no longer seemed in books before.
Read Online or Download Algebraic cycles, sheaves, shtukas, and moduli PDF
Similar algebraic geometry books
An Invitation to Algebraic Geometry
This can be a description of the underlying ideas of algebraic geometry, a few of its very important advancements within the 20th century, and a few of the issues that occupy its practitioners at the present time. it truly is meant for the operating or the aspiring mathematician who's unexpected with algebraic geometry yet needs to achieve an appreciation of its foundations and its targets with not less than necessities.
The Geometry of Topological Stability
In proposing a close research of the geometry and topology of various sessions of "generic" singularities, Geometry of Topological balance bridges the space among algebraic calculations and continuity arguments to aspect the mandatory and adequate stipulations for a C (infinity) to be C0-stable. all through, the authors masterfully learn this significant topic utilizing effects culled from a extensive variety of mathematical disciplines, together with geometric topology, stratification conception, algebraic geometry, and commutative algebra.
Arithmetic of p-adic Modular Forms
The valuable subject of this learn monograph is the relation among p-adic modular varieties and p-adic Galois representations, and particularly the idea of deformations of Galois representations lately brought through Mazur. The classical concept of modular kinds is believed recognized to the reader, however the p-adic concept is reviewed intimately, with considerable intuitive and heuristic dialogue, in order that the e-book will function a handy element of access to investigate in that sector.
An invitation to arithmetic geometry
During this quantity the writer offers a unified presentation of a few of the fundamental instruments and ideas in quantity concept, commutative algebra, and algebraic geometry, and for the 1st time in a booklet at this point, brings out the deep analogies among them. The geometric perspective is under pressure during the booklet.
- Introduction To Coding Theory And Algebraic Geometry
- Algebraic geometry III. Complex algebraic varieties. Algebraic curves and their Jacobians
- Geometry and Complex Variables
- Modular forms and Fermat's last theorem
Extra resources for Algebraic cycles, sheaves, shtukas, and moduli
Sample text
If 0 < m < n we can view Om as a sheaf of On -modules. 2. 1. If 1 ≤ i ≤ n then every vector bundle on Ci can be extended to a vector bundle on Cn . 2. Parametrization. Let E be a vector bundle on Cn , and En−1 = E|Cn−1 , E = E|C . Then we have an exact sequence 0 −→ En−1 ⊗ On−1 (−C) −→ E −→ E −→ 0 , (with On−1 (−C) = OS (−C)|Cn−1 ). Conversely, let En−1 be a vector bundle on Cn−1 and E = En−1|C . Then using suitable locally free resolutions on Cn one can find canonical isomorphisms E ∗ ⊗ E ⊗ Ln−1 , Hom(E, En−1 ⊗ On−1 (−C)) E ∗ ⊗ E.
Faisceaux semi-stables de dimension 1 sur le plan projectif. Revue roumaine de math. pures et appliqu´ees 38 (1993), 635–678. [13] Maruyama, M. Moduli of stable sheaves I. J. Math. Kyoto Univ. 17 (1977), 91–126. Moduli Spaces of Coherent Sheaves on Multiples Curves 43 [14] Maruyama, M. Moduli of stable sheaves II. J. Math. Kyoto Univ. 18 (1978), 577–614. , Trautmann, G. Multiple Koszul structures on lines and instanton bundles. Intern. Journ. of Math. 5 (1994), 373–388. T. Moduli of representations of the fundamental group of a smooth projective variety I.
Then there exist integers m, q, n1 , . . , np such that p Ini ,P M ⊕ mO2,P ⊕ qOC,P . 3. Deformations of sheaves If E is a coherent sheaf on C then the canonical morphism Ext1On (E, E) −→ Ext1OS (E, E) is an isomorphism. Let M be a O2,P -module, M2 ⊂ M its canonical filtration. Let r0 (M ) = rk(M2 ). Then we have R(M ) ≥ 2r0 (M ). If M is quasi free then we have R(M ) = 2r0 (M ) if and only if M is free. 1. Let M be a quasi free O2,P -module, and r0 an integer such that 0 < 2r0 ≤ R(M ). Then M can be deformed in quasi free modules N such that r0 (N ) = r0 if and only if r0 ≥ r0 (M ).
