TY - JOUR

T1 - 64 lines on smooth quartic surfaces

AU - Schütt, Matthias

AU - Rams, Slawomir

N1 - Funding information: We are indebted to Wolf Barth for sharing his insights on the subject starting more than 10 years ago. Thanks to Achill Schürmann for helpful discussions on quadratic forms. We are grateful to Igor Dolgachev, Duco van Straten and the anonymous referee for their valuable comments. This project was started in March 2011 when Schütt enjoyed the hospitality of the Jagiellonian University in Krakow. Special thanks to S?awomir Cynk. Funding by ERC StG 279723 (SURFARI) and NCN Grant N N201 608040 (S. Rams) is gratefully acknowledged.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - Let k be a field of characteristic p≥0 with p≠2,3. We prove that there are no geometrically smooth quartic surfaces S⊂P k3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on S

AB - Let k be a field of characteristic p≥0 with p≠2,3. We prove that there are no geometrically smooth quartic surfaces S⊂P k3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on S

KW - math.AG

KW - math.NT

KW - 14J25, 14J28, 14J70, 14N25

KW - K3 surfaces

KW - elliptic fibration

KW - positive characteristic

KW - 14J25

KW - 14N25

KW - 14J28

KW - 14J70

UR - http://www.scopus.com/inward/record.url?scp=84939943235&partnerID=8YFLogxK

U2 - 10.1007/s00208-014-1139-y

DO - 10.1007/s00208-014-1139-y

M3 - Article

VL - 362

SP - 679

EP - 698

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -