- 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: fibers introduces interesting featu
- 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 and 130:
119 [28] D. Bayer and M. Stillman,