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 A266322 Genera of complete intersection curves. 1
 0, 1, 3, 4, 5, 6, 9, 10, 13, 15, 16, 17, 19, 21, 25, 28, 31, 33, 36, 37, 41, 45, 46, 49, 51, 55, 61, 64, 65, 66, 73, 76, 78, 81, 85, 91, 97, 99, 100, 101, 105, 106, 109, 113, 120, 121, 129, 136, 141, 144, 145, 148, 153, 161, 163, 166, 169, 171, 176, 181, 190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Pieter Belmans, Table of n, a(n) for n = 1..215 P. Deligne and N. Katz, Groupes de monodromie en géométrie algébrique (SGA 7 II), Springer-Verlag, 1973, pages 39-61. PROG (Sage) def genus(degrees):   n = len(degrees) + 1   return 1 + 1 / 2 * prod(degrees) * (sum(degrees) - n - 1) """ Generate a list of all genera of complete intersection curves up to a cutoff. Observe that the genus strictly increases if we increase the degree of a defining equation, while adding a hyperplane section keeps the degree fixed. So we can obtain all low genera starting from the line in P^2, and increasing the number of equations and the degrees of the defining equations """ def listOfGenera(cutoff):   queue = [(1, )]   genera = []   while len(queue) > 0:     degrees = queue.pop()     g = genus(degrees)     if g < cutoff:       # if we haven't found this one yet we add it to the list       if g not in genera:         genera.append(g)         # use this to get information on how to realize a curve         # print (g, degrees)       # add all valid (d_1, ..., d_i+1, ..., d_{n-1})       for i in range(len(degrees)):         new = list(degrees)         new[i] = new[i] + 1         # we only look at increasing lists of degrees         if sorted(new) == new:           queue.append(tuple(new))       # add (d_1, ..., d_{n-1}, 2): with , 1 at the end genus is constant       queue.append(degrees + (2, ))   return sorted(genera) CROSSREFS Sequence in context: A129948 A050414 A342469 * A136681 A206330 A104373 Adjacent sequences:  A266319 A266320 A266321 * A266323 A266324 A266325 KEYWORD nonn AUTHOR Pieter Belmans, Dec 27 2015 STATUS approved

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Last modified September 18 11:20 EDT 2021. Contains 347518 sequences. (Running on oeis4.)