- Page 1 and 2:
DERIVED CATEGORIES OF TWISTED SHEAV
- Page 3 and 4:
DERIVED CATEGORIES OF TWISTED SHEAV
- Page 5 and 6:
Tuturor celor din care am fost făc
- Page 7 and 8:
Table of Contents
- Page 9 and 10:
List of Figures 6.
- Page 11 and 12:
Introduction and Overview Twisted <
- Page 13 and 14:
twisted by α ∈
- Page 15 and 16:
fibers introduces interesting featu
- Page 17 and 18:
Chapter 1 Twisted Sheaves In this c
- Page 19 and 20:
to be H2 an(X, O∗ X ). If we do n
- Page 21 and 22:
is bijective. Then A is called an A
- Page 23 and 24:
such that α = δa and β = δb. Si
- Page 25 and 26:
Lemma 1.2.3. Let α ∈ Č2 (X, O
- Page 27 and 28:
Proof. Let U ′
- Page 29 and 30:
Proof. Since E and
- Page 31 and 32:
Proof. Follows fro
- Page 33 and 34:
Definition 1.3.12. Let A be a ring.
- Page 35 and 36:
Definition 1.3.18. Two R-algebras A
- Page 37 and 38:
property “free on stalks” for t
- Page 39 and 40:
2.2 The Derived Category and Derive
- Page 41 and 42:
to reduce to the case when F · als
- Page 43 and 44:
So assume n > 0, and as before cons
- Page 45 and 46:
Proposition 2.3.4. Let f : X → Y
- Page 47 and 48:
2.4 Duality for Proper Smooth Morph
- Page 49 and 50:
complex manifolds, and let X × Y
- Page 51 and 52:
if v consists only of</stro
- Page 53 and 54:
The reason for the notation is that
- Page 55 and 56:
Proof. The first s
- Page 57 and 58:
which by definition associates to a
- Page 59 and 60:
Part II Applications 49
- Page 61 and 62:
X which would intersect a general f
- Page 63 and 64:
to C ′ , independent of</
- Page 65 and 66:
Jij → S. This means that if Fij w
- Page 67 and 68:
Li = ρ∗ i L −1 |Xi . Then we h
- Page 69 and 70:
It is easy to see that ϕi(ti) = [O
- Page 71 and 72:
Remark 4.5.3. Note that we have fix
- Page 73 and 74:
allow us to get X; however, finding
- Page 75 and 76:
endowed with the product ((r, l, s)
- Page 77 and 78:
Theorem 5.1.10. Under the hypothese
- Page 79 and 80: groups of differen
- Page 81 and 82: Let c be the image of</stro
- Page 83 and 84: Proof. Trivial cha
- Page 85 and 86: and therefore rk(V ) = (v(V ), (0,
- Page 87 and 88: for some k ≫ 0. By the same argum
- Page 89 and 90: and therefore Now consider the map
- Page 91 and 92: In order to identify the kernel, no
- Page 93 and 94: for all F , G stable sheave
- Page 95 and 96: Chapter 6 Elliptic Calabi-Yau Three
- Page 97 and 98: Definition 6.1.2. A projective morp
- Page 99 and 100: Example 6.2.1. We’ve already seen
- Page 101 and 102: contract 45 curves 2H+D-E contract
- Page 103 and 104: Remark 6.3.2. This theorem basicall
- Page 105 and 106: But this is impossible, because the
- Page 107 and 108: We have H 0 (C, IQ) = 0 and χ(IQ)
- Page 109 and 110: Having fixed a smooth point P ∈ C
- Page 111 and 112: 101 Proof. Since X
- Page 113 and 114: 103 Therefore, α can be represente
- Page 115 and 116: Corollary 6.5.6. Under the hypothes
- Page 117 and 118: 107 Remark 6.6.4. We could also pro
- Page 119 and 120: 109 where the intersection form on
- Page 121 and 122: 111 where ci = ci(i∗U · ). Obvio
- Page 123 and 124: 113 One space of i
- Page 125 and 126: Open Questions and Further Directio
- Page 127 and 128: Bibliography [1] Aspinwall, P., Mor
- Page 129: 119 [28] D. Bayer and M. Stillman,