Download PDF by C. Herbert Clemens: A scrapbook of complex curve theory

By C. Herbert Clemens

ISBN-10: 0306405369

ISBN-13: 9780306405365

This advantageous ebook through Herb Clemens speedy grew to become a favourite of many advanced algebraic geometers whilst it was once first released in 1980. it's been well liked by rookies and specialists ever on the grounds that. it's written as a publication of "impressions" of a trip throughout the thought of complicated algebraic curves. Many themes of compelling attractiveness ensue alongside the way in which. A cursory look on the matters visited finds an it seems that eclectic choice, from conics and cubics to theta services, Jacobians, and questions of moduli. by way of the tip of the e-book, the subject matter of theta services turns into transparent, culminating within the Schottky challenge. The author's reason was once to encourage extra learn and to stimulate mathematical job. The attentive reader will study a lot approximately complicated algebraic curves and the instruments used to review them. The booklet should be specifically necessary to a person getting ready a path concerning complicated curves or an individual drawn to supplementing his/her studying

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Ba] W. Barth, Fortsetzung meromorpher Funktionen in Tori und komplex-projektiven Räumen, Invent. Math. 5 (1968), 42–62. [Bo] A. Borel, Linear algebraic groups, W. A. Benjamin, New York–Amsterdam 1969. [Ch1] W. L. Chow, On meromorphic maps of algebraic varieties, Ann. of Math. 89 (1969), 391–403. [Ch2] W. L. Chow, Formal functions on homogeneous spaces, Invent. Math. 86 (1986), 115–130. [De1] O. Debarre, Sur un théorème de connexité de Mumford pour les espaces homogènes, Manuscripta Math. 89 (1996), 407–425.

Extensions 32 2. 1. 2. 3. Hodge conjecture for singular varieties 38 3. 1. 2. 3. 4. Local-to-global properties 45 4. 1. 2. Coniveau filtration 49 Algebraic Geometry. A Volume in Memory of Paolo Francia M. C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, C. ) © Walter de Gruyter 2002 26 L. 3. 4. K-cohomology and motivic cohomology 5. 1. 2. Srinivas’ example 51 53 55 55 56 0. Introduction Let X be an algebraic C-scheme. The singular cohomology groups H ∗ (X, Z(·)) carry a mixed Hodge structure, see [11, III].

Dieudonné, Eléments de Géométrie Algébrique I, SpringerVerlag, Berlin–Heidelberg–New York 1971. [EGAIII] A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique III, Inst. Hautes Études Sci. Publ. Math. 11 (1961). [EGAIV] A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique IV (2), Inst. Hautes Études Sci. Publ. Math. 24 (1965). [SGA1] A. Grothendieck, Revêtements étales et groupe fondamental, Lecture Notes in Math. 224 , Springer-Verlag, Berlin 1971. [SGA2] A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, North Holland, Amsterdam 1968.

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A scrapbook of complex curve theory by C. Herbert Clemens

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