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¡ºº¹¼Ò´Ù¾çü¡»´Â ¡´±âº»°³³ä¡µ, ¡´ÄÚÈ£¸ô·ÎÁö¡µ, ¡´º¹¼Òº¤Å¸¹øµéÀÇ ±âÇÏ¡µ, ¡´ÄÚÈ£¸ô·ÎÁö ºÐ¸®¡µ, ¡´º¹¼Ò±Û¶ó½º¸¸´Ù¾çü¡µ, ¡´°í´ÙÀ̶ó ¸ÅÀ塵 µîÀ» ¼ö·ÏÇÏ°í Àִ åÀÌ´Ù.
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CHAPTER 01 ±âº»°³³ä
1.1 ´Ù¾çü(Manifolds) 1
1.2 º¹¼Ò´Ù¾çü(Complex Manifolds) 4
1.3 º¤Å͹øµé(Vector Bundles) 13
1.4 ´Ù¾çüÀÇ ¸ÅÀå(Embedding of Manifolds) 17
1.5 µå¶÷ÄÚÈ£¸ô·ÎÁö(de Rham Cohomology) 19
1.6 Ư¼º·ù(Characteristic Classes) 25
CHAPTER 02 ?ÄÚÈ£¸ô·ÎÁö
2.1 ?(Sheaf) 31
2.2 ?ÄÚÈ£¸ô·ÎÁö(Sheaf Cohomology) 36
CHAPTER 03 º¹¼Òº¤Å¸¹øµéÀÇ ±âÇÏ
3.1 º¹¼Òº¤Å¸¹øµé(Complex Vector Bundles) 43
3.2 °î·ü(Curvature) 48
3.3 õ-º£ÀÏÀÌ·Ð(Chern-Weil Theory) 53
CHAPTER 04 ÄÚÈ£¸ô·ÎÁö ºÐ¸®
4.1 ¸®¸¸´Ù¾çüÀÇ Á¶ÈÆû (Harmonic Forms on Riemannian Manifolds) 60
4.2 Çæ¹Ì¼Ç º¹¼Ò´Ù¾çüÀÇ Á¶ÈÆû (Harmonic Forms on Hermitian Complex Manifolds)69
4.3 ÄÌ·¯´Ù¾çüÀÇ ÄÚÈ£¸ô·ÎÁöºÐ¸® (Cohomology Decompositions of KahlerManifolds)
CHAPTER 05 º¹¼Ò±Û¶ó½º¸¸´Ù¾çü
5.1 ±Û¶ó½º¸¸´Ù¾çüÀÇ Á¤ÀÇ(Definition of Grassmann Manifold) 86
5.2 ½´º§Æ®¹ú¶óÀ̾îƼ(Schubert Variety) 89
5.3 ±Û¶ó½º¸¸´Ù¾çüÀÇ ÀÀ¿ë (Applications of Grassmann Manifold) 95
CHAPTER 06 °í´ÙÀ̶ó ¸ÅÀå
6.1 È£Áö´Ù¾çü(Hodge Ma...nifolds) 100
6.2 °í´ÙÀ̶ó ¼Ò¸êÁ¤¸®(Kodaira Vanishing Theorem) 107
6.3 ºí·Î¿ì¾÷(Blow-up) 112
6.4 °í´ÙÀ̶ó ¸ÅÀåÁ¤¸®(Kodaira Embedding Theorem) 118
CHAPTER 07 È£ÁöÃßÃø
7.1 È£Áö±¸Á¶(Hodge Structure) 130
7.2 ?¼ÅÃ÷Á¤¸®(Lefschetz Theorem) 134
7.3 È£Áö·ù¿Í ´ë¼öÀû½ÎÀÌŬ·ù (Hodge Class and Algebraic Cycle Class) 137
7.4 ¾Ë·ÁÁø °á°ú(Known Results) 141
CHAPTER 08 ?¼ÅÃ÷ÃßÃø
8.1 ´ë°¢ÄÚÈ£¸ô·ÎÁö·ù(Diagonal Cohomology Class) 146
8.2 ?¼ÅÃ÷ µ¿Çü¸Ê(Lefschetz Isomorphism) 153
8.3 ?¼ÅÃ÷ÃßÃø(Lefschetz Conjecture) 160
ºÎ·Ï
ºÎ·Ï A. Çæ¹Ì¼Ç¿Ü´ë¼ö »óÀÇ ¸®´ë¼öÇ¥Çö(Representation) 168
A1. ¸®´ë¼öÀÇ Ç¥Çö(Representation) 168
A2. Çæ¹Ì¼Ç¿Ü´ë¼ö(Hermitian Exterior Algebra) »óÀÇ Ç¥Çö 181
ºÎ·Ï B. º¹¼Ò±¸Á¶(Complex Structures) 187
B1. ¸ÞÆ®¸¯(Metric), º¹¼Ò±¸Á¶(Complex Structure), ±âº»Æû(Fundamental Form)»çÀÌ °ü°è 187
B2. Áغ¹¼Ò´Ù¾çü(Almost Complex Manifolds) 192
B3. º¹¼Ò´Ù¾çü(Complex Manifolds) 196
B4. ÄÌ·¯´Ù¾çü(Kahler Manifolds) 204
B5. È£Áö´Ù¾çü(Hodge Manifolds) 209
ºÎ·Ï C. ¼öÇÐÀÚµé(Mathematicians) 212
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