SCVeamer 1.4 prototype — English edition

Credits and references

Back to the sample guide · Open sample slides

THIS ENGLISH SAMPLE LECTURE

Intensive Lecture -- Day 1: Complex Analysis in Several Variables. English version of the Japanese version 1.3 lecture aligned with the R135 notes, including the boundary Levi form and holomorphic extension. There are 46 logical slides, 76 display states and 135 planned minutes (14:55-17:10). The title remains the lecture title inside the deck; the website presents it as sample slides. The final question compares strong 1-completeness / strong 1-convexity with weak 1-completeness.

The mathematical source, timing and printed explanations are in talk.tex. The kit includes two theme files, eight static PDF figures, the supplied analytic-disc illustration, supplementary slide metadata and these credits. The finished HTML embeds all three English interactive interfaces. The English source uses LuaLaTeX and Latin Modern fonts, without Japanese font packages.

LECTURE AUTHOR AND SOURCE NOTES

Takayuki Koike, University of Tsukuba. Complex Analytic Geometry and Dynamics on Analytic Neighborhood Spaces. Supplied R135 file: ANNS_R135_FULL (1).pdf, 916 pages. Version shown on its title page: Version v0.4, September 26, 2026.

Reference map: Chapter I, Section 9: one-variable review and subharmonic functions. Chapter I, Section 8.7: complex derivatives and the Laplacian convention. Chapter I, Sections 6.4-6.5: distributions and function-space topologies. Chapter III, Sections 1.1-1.2, 2.1, 2.7 and 2.10: holomorphic functions, complex geometry, plurisubharmonicity and pseudoconvexity. Observation III.2.148, printed p. 492 / PDF p. 510: boundary Levi form and holomorphic functions. Lemma III.1.14 supplies the background for the normal form, which is used without proof in this lecture. Figure III.4, printed p. 493 / PDF p. 511: analytic-disc configuration.

The content continues to reflect the 24 annotations on previously supplied lecture slides. The original notes and annotated PDFs are not redistributed in the kit; the lecture reorganizes their material for this presentation.

HISTORICAL REFERENCE: RYOKUINZU AND OKA

Toshio Nishino, "Oka Kiyoshi sensei no sugaku" [The Mathematics of Professor Kiyoshi Oka], Sugaku 33(2) (1981), 171-178 (in Japanese). The discussion of Ryokuinzu is on pp. 174-175; the short quotation is on p. 175. The English quotation in the slide is identified as a translation. https://doi.org/10.11429/sugaku1947.33.171

SUPPLEMENT FOR OKA'S LEMMA

Jean-Pierre Demailly, Complex Analytic and Differential Geometry (2012), Chapter I, Theorem (7.2)(e), p. 54. https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf

SUPPLEMENT FOR LOCAL HOLOMORPHIC EXTENSION

Jiri Lebl, Tasty Bits of Several Complex Variables, version 4.4, Theorem 2.3.11, printed pp. 75-76. https://jirka.org/scv/scv.pdf Observation III.2.148 directly gives a uniform bound at the disc centers and the resulting failure of holomorphic convexity. The local extension argument is a separate supplement using a Cauchy integral and parameter variation. The positive-Levi function 1/w is local, not asserted to exist globally.

INTERACTIVE EXAMPLES AND NOTATION

The interfaces originate in the Project Holomorphonautica materials supplied on 22 October 2026. Their version 1.2 behavior is retained, with English text and English language defaults in this edition. The kit embeds resources/games/ in each generated HTML file; no external game download is needed for viewing.

Lecture mode selects a registered example by ID. It offers a formula display, question/answer-and-explanation switch, interactive controls and reset. It does not use scoring, random next questions or saved progress. Existing credits inside the three interfaces are retained.

Examples used: Subharmonic?: std-b03, std-b02, std-i02. Ryokuinzu: lecture-ball, lecture-polydisc, n18. Plurisubharmonic?: N01, A03. The lecture-ball and lecture-polydisc IDs are existing fixed lecture examples. The three Ryokuinzu questions and observation instructions are stored in lecture-plan.json. The kit manual lists all 194 registered examples.

Notation follows R135: the negative-sign Delta, H(phi), Psh(Omega), sqrt(-1), roman Re and Im, and Lebesgue measure d lambda. The SH interface's Laplacian corresponds to -Delta; the PSH interface's Levi matrix is H(u), the complex Hessian of the function. The boundary Levi form is its restriction to the complex tangent space when the function defines a boundary.

FIGURES

The eight existing static PDF figures in assets/ show surfaces, complex-line restrictions and domain fibers. They already use English or mathematical labels and are preserved. The source includes editable TikZ sketches of circles, overlapping domains, tangent vectors, sublevel sets, compact fibers and a locally supporting hypersurface. These are ordinary lines, circles, arrows and labels; no image-generation application is needed to rebuild them.

assets/levi-analytic-discs.png is the supplied illustration, preserved unchanged. It corresponds to R135 Figure III.4 and illustrates the relationship between discs, their centers and their boundary circles in Observation III.2.148. Its labels are mathematical and need no translation. Matplotlib is unnecessary for normal rebuilding because the figure assets are included.

OUTPUTS AND PRESENTATION SETTINGS

SCVeamer renders the typeset PDF pages as PNG using pypdfium2/PDFium and Pillow, reads PDF structure with pypdf, and packages them with interactive examples and a player in a self-contained index.html. talk.pdf contains every display state; handout.pdf contains the final state of each logical slide. This sample disables speaker notes and does not generate a speaker guide. Its blue theme and lack of footer branding are unchanged. Planned finish times follow the start time and per-slide minutes written in talk.tex. They are a schedule, not an elapsed-time timer.